Edit Profile (opens in new tab) Gauthier, Paul M. Compute Distance To: Compute Author ID: gauthier.paul-m Published as: Gauthier, P. M.; Gauthier, Paul M.; Gauthier, Paul; Gauthier, P. Documents Indexed: 174 Publications since 1968, including 2 Books 4 Contributions as Editor · 1 Further Contribution Biographic References: 1 Publication Co-Authors: 66 Co-Authors with 133 Joint Publications 1,043 Co-Co-Authors all top 5 Co-Authors 42 single-authored 15 Hengartner, Walter 10 Boivin, André 9 Bagby, Thomas 9 Chen, Huaihui 8 Brown, Leon 7 Nestoridis, Vassili 7 Paramonov, Peter V. 6 Ow, Wellington Ham 5 Manolaki, Myrto 5 Sharifi, Fatemeh 5 Zeron, Eduardo Santillan 4 Goldstein, Myron 4 Pouryayevali, Mohamad Reza 4 Tarkhanov, Nikolai N. 3 Dufresnoy, Alain 3 Dwilewicz, Roman J. 3 Falcó, Javier 3 Frih, El Mostapha 3 Seidel, Wladimir 3 Xiao, Jie 3 Zwick, Daniel S. 2 Arakelyan, N. U. 2 Armitage, David H. 2 Aron, Richard Martin 2 Bayart, Frédéric 2 Donzelli, Fabrizio 2 Maestre, Manuel 2 Mashreghi, Javad 2 Rubel, Lee Albert 2 Sabidussi, Gert 2 Schmieder, Gerald 2 Walsh, Joseph Leonard 2 Zhu, Changzhong 1 Arakelyan, N. O. 1 Ascah-Coallier, Isabelle 1 Bensouda, Charaf 1 Berberyan, Samvel L. 1 Blanchet, Pierre 1 Chacrone, Seddik 1 Charpentier, Stéphane 1 Clouâtre, Raphaël 1 Cornea, Aurel 1 Daepp, Ulrich 1 Daghighi, Abtin 1 Fournier, John J. F. 1 Gaier, Dieter 1 Gorkin, Pamela B. 1 Grosse-Erdmann, Karl-Goswin 1 Heinonen, Juha 1 Kienzle, Julie 1 Knese, Greg 1 Labreche, M. 1 Ladouceur, Stephane 1 Marden, Morris 1 Melnikov, Mark S. 1 Mortini, Raymond 1 Nersessian, Ashot H. 1 Ngô van Quê 1 Olivi-Tran, Nathalie 1 Papadopoulos, Athanase 1 Rahman, Qazi Ibadur 1 Ransford, Thomas J. 1 Rivlin, Theodore Joseph 1 Roth, Alice 1 Saff, Edward Barry 1 Schempp, Walter Johannes 1 Sewell, Walter Edwin 1 St-Amant, Simon 1 Stray, Arne 1 Tamptse, Innocent 1 Turcotte, Jérémie 1 Widder, David Vernon 1 Woodworth, Jennifer 1 Xarles, Xavier all top 5 Serials 26 Canadian Mathematical Bulletin 18 Canadian Journal of Mathematics 8 Complex Variables. Theory and Application 7 Computational Methods and Function Theory 5 Journal of Approximation Theory 5 Proceedings of the American Mathematical Society 4 Journal of Mathematical Analysis and Applications 4 Transactions of the American Mathematical Society 4 Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 3 Journal d’Analyse Mathématique 3 Journal of the London Mathematical Society. Second Series 2 Annales Polonici Mathematici 2 Nagoya Mathematical Journal 2 Constructive Approximation 2 Izvestiya Akademii Nauk Armyanskoi SSR. Matematika 2 Izvestiya: Mathematics 2 Annals of Mathematics. Second Series 2 Analysis (München) 2 Complex Variables and Elliptic Equations 2 Annales Academiae Scientiarum Fennicae. Series A I 1 Mathematical Notes 1 Rocky Mountain Journal of Mathematics 1 Russian Mathematical Surveys 1 The Mathematical Intelligencer 1 Advances in Mathematics 1 Annales des Sciences Mathématiques du Québec 1 Archiv der Mathematik 1 Bulletin of the London Mathematical Society 1 Bulletin Mathématique de la Société des Sciences Mathématiques de la République Socialiste de Roumanie. Nouvelle Série 1 Colloquium Mathematicum 1 Journal of Mathematics of Kyoto University 1 Mathematische Annalen 1 Michigan Mathematical Journal 1 Results in Mathematics 1 Soviet Journal of Contemporary Mathematical Analysis. Armenian Academy of Sciences 1 Bulletin de la Classe des Sciences. 5e Série 1 Doklady Bolgarskoĭ Akademii Nauk 1 L’Enseignement Mathématique. 2e Série 1 Journal of the Australian Mathematical Society. Series A 1 Methods and Applications of Analysis 1 Sbornik: Mathematics 1 Oberwolfach Reports 1 Annali della Scuola Normale Superiore di Pisa. Scienze Fisiche e Matematiche. III. Ser 1 Fields Institute Communications 1 NATO ASI Series. Series C. Mathematical and Physical Sciences 1 Proceedings of the Steklov Institute of Mathematics 1 NATO Science Series II: Mathematics, Physics and Chemistry 1 Zbirnyk Prats’ Instytutu Matematyky NAN Ukraïny 1 Albanian Journal of Mathematics 1 Advanced Studies in Theoretical Physics 1 Analysis and Mathematical Physics 1 Annales Mathématiques du Québec 1 Complex Analysis and its Synergies all top 5 Fields 105 Functions of a complex variable (30-XX) 48 Potential theory (31-XX) 35 Several complex variables and analytic spaces (32-XX) 32 Approximations and expansions (41-XX) 15 Number theory (11-XX) 10 Partial differential equations (35-XX) 10 Functional analysis (46-XX) 4 General and overarching topics; collections (00-XX) 4 History and biography (01-XX) 3 Operator theory (47-XX) 2 Measure and integration (28-XX) 1 Algebraic geometry (14-XX) 1 Real functions (26-XX) 1 Differential geometry (53-XX) 1 General topology (54-XX) 1 Global analysis, analysis on manifolds (58-XX) 1 Probability theory and stochastic processes (60-XX) 1 Numerical analysis (65-XX) 1 Relativity and gravitational theory (83-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH Open 111 Publications have been cited 511 times in 350 Documents Cited by ▼ Year ▼ Bloch constants for planar harmonic mappings. Zbl 0956.30012Chen, Huaihui; Gauthier, P. M.; Hengartner, W. 56 2000 Bloch constants in several variables. Zbl 0966.32002Chen, Huaihui; Gauthier, P. M. 22 2001 Composition operators on \(\mu\)-Bloch spaces. Zbl 1171.47020Chen, Huaihui; Gauthier, Paul 19 2009 On Bloch’s constant. Zbl 0864.30025Chen, Huaihui; Gauthier, Paul M. 19 1996 The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings. Zbl 1234.30024Chen, Huaihui; Gauthier, Paul M. 17 2011 BiBloch-type maps: existence and beyond. Zbl 1026.30035Gauthier, Paul M.; Xiao, Jie 12 2002 Boundedness from below of composition operators on \(\alpha\)-Bloch spaces. Zbl 1148.30017Chen, Huaihui; Gauthier, Paul 12 2008 Subharmonic extensions and approximations. Zbl 0790.31001Gauthier, P. M. 11 1994 On uniform approximation by \(n\)-analytic functions on closed sets in \(\mathbb C\). Zbl 1069.30076Boivin, A.; Gauthier, P. M.; Paramonov, P. V. 11 2004 Recent developments in harmonic approximation, with applications. Zbl 0859.31001Armitage, D. H.; Gauthier, P. M. 10 1996 Uniform approximation on closed sets by harmonic functions with Newtonian singularities. Zbl 0525.31002Gauthier, P. M.; Goldstein, M.; Ow, W. H. 9 1983 Local harmonic majorants of functions subharmonic in the unit disc. Zbl 0279.31001Gauthier, P. M.; Hengartner, Walter 9 1973 A criterion for normalcy. Zbl 0157.39802Gauthier, P. 9 1968 Approximation by harmonic functions of closed subsets of Riemann surfaces. Zbl 0671.30037Bagby, Thomas; Gauthier, P. M. 9 1988 Approximation on closed sets by analytic or meromorphic solutions of elliptic equations and applications. Zbl 1022.30043Boivin, André; Gauthier, Paul M.; Paramonov, Petr V. 9 2002 Uniform approximation on unbounded sets by harmonic functions with logarithmic singularities. Zbl 0447.30035Gauthier, P. M.; Goldstein, M.; Ow, W. H. 9 1980 Dirichlet approximation and universal Dirichlet series. Zbl 1386.30057Aron, Richard M.; Bayart, Frédéric; Gauthier, Paul M.; Maestre, Manuel; Nestoridis, Vassili 9 2017 Approximation of and by the Riemann zeta-function. Zbl 1284.11122Gauthier, Paul M. 8 2010 Approximation of a function and its derivatives by entire functions of several variables. Zbl 0641.32011Frih, El Mostapha; Gauthier, Paul M. 7 1988 Universal overconvergence of homogeneous expansions of harmonic functions. Zbl 1132.31002Gauthier, Paul M.; Tamptse, Innocent 7 2006 Continuous boundary behaviour for functions defined in the open unit disc. Zbl 0307.30031Brown, Leon; Gauthier, P. M.; Hengartner, Walter 7 1975 Uniform approximation. Zbl 0810.30001Gauthier, Paul M. 7 1994 Asymptotic maximum principles for subharmonic and plurisubharmonic functions. Zbl 0661.31007Gauthier, P. M.; Grothmann, R.; Hengartner, W. 7 1988 Density of polynomials in classes of functions on products of planar domains. Zbl 1331.46044Gauthier, P. M.; Nestoridis, V. 6 2016 Uniform approximation on closed sets by functions analytic on a Riemann surface. Zbl 0322.30034Gauthier, P. M.; Hengartner, W. 6 1975 Possibility of uniform rational approximation in the spherical metric. Zbl 0322.30036Gauthier, P. M.; Roth, A.; Walsh, Joseph L. 6 1976 Complex approximation and simultaneous interpolation on closed sets. Zbl 0338.30026Gauthier, P. M.; Hengartner, W. 6 1977 Approximation by meromorphic functions with Mittag-Leffler type constraints. Zbl 0994.30022Gauthier, P. M.; Pouryayevali, M. R. 6 2001 Approximation on arcs and dendrites going to infinity in \(\mathbb{C}^n\). Zbl 1012.32003Gauthier, P. M.; Zeron, E. S. 6 2002 Approximation by the Riemann zeta-function. Zbl 1101.30038Gauthier, P. M.; Tarkhanov, N. 6 2005 The existence of universal inner functions on the unit ball of \(\mathbb C^n\). Zbl 1105.32003Gauthier, P. M.; Xiao, J. 6 2005 Approximation by (pluri) subharmonic functions: Fusion and localization. Zbl 0782.31001Gauthier, P. M. 5 1992 Lectures on several complex variables. Zbl 1310.32001Gauthier, Paul M. 5 2014 Small perturbations of the Riemann zeta function and their zeros. Zbl 1051.11046Gauthier, Paul M.; Zeron, Eduardo S. 5 2004 Approximation uniforme qualitative sur des ensembles non bornes. Zbl 0482.30028Gauthier, Paul M.; Hengartner, Walter 5 1982 Uniform approximation on closed sets by solutions of elliptic partial differential equations. Zbl 0569.35022Dufresnoy, A.; Gauthier, P. M.; Ow, W. H. 4 1986 Uniform approximation by global harmonic functions. Zbl 0759.41017Bagby, T.; Gauthier, P. M. 4 1992 Behavior of normal meromorphic functions on the maximal ideal space of \(H^ \infty\). Zbl 0219.46040Brown, L.; Gauthier, P. M. 4 1971 Some applications of Arakelian’s approximation theorems to the theory of cluster sets. Zbl 0233.30029Gauthier, P.; Seidel, W. 4 1972 Failure of Landau’s theorem for quasiconformal mappings of the disc. Zbl 1074.30019Gauthier, P. M.; Pouryayevali, M. R. 4 2004 Meromorphic uniform approximation on closed subsets of open Riemann surfaces. Zbl 0409.30033Gauthier, P. M. 4 1979 Approximating functions by the Riemann zeta-function and by polynomials with zero constraints. Zbl 1264.30023Gauthier, Paul M. 4 2012 Zero-free polynomial approximation on a chain of Jordan domains. Zbl 1293.30074Gauthier, Paul M.; Knese, Greg 4 2012 Global holomorphic approximations of CR functions on CR manifolds. Zbl 0548.32011Dwilewicz, Roman; Gauthier, P. M. 3 1985 Note on the decay of solutions of elliptic equations. Zbl 0563.35028Armitage, D. H.; Bagby, Thomas; Gauthier, P. M. 3 1985 Mergelyan’s theorem with polynomials non-vanishing on unions of sets. Zbl 1295.30087Andersson, J.; Gauthier, P. M. 3 2014 Perturbations of \(L\)-functions with or without non-trivial zeros off the critical line. Zbl 1250.11084Gauthier, Paul M.; Xarles, Xavier 3 2009 Mittag-Leffler theorems on Riemann surfaces and Riemannian manifolds. Zbl 0914.30033Gauthier, Paul M. 3 1998 Holomorphic functionals on open Riemann surfaces. Zbl 0321.46032Gauthier, P. M.; Rubel, L. A. 3 1976 Tangential approximation by entire functions and functions holomorphic in a disc. Zbl 0189.36006Gauthier, P. 3 1969 Harmonic approximation on closed subsets of Riemannian manifolds. Zbl 0806.31003Bagby, Thomas; Gauthier, Paul M. 3 1994 Holomorphic and harmonic approximation on Riemann surfaces. Zbl 1017.30044Boivin, André; Gauthier, Paul M. 3 2001 On strongly normal functions. Zbl 0879.30019Chen, Huaihui; Gauthier, Paul M. 3 1996 A function algebra providing new Mergelyan type theorems in several complex variables. Zbl 1462.32002Falcó, Javier; Gauthier, Paul M.; Manolaki, Myrto; Nestoridis, Vassili 3 2021 Weighted Hardy spaces for the unit disc: approximation properties. Zbl 1146.30034Boivin, André; Gauthier, Paul M.; Zhu, Changzhong 3 2007 Approximation by translates of Taylor polynomials of the Riemann zeta function. Zbl 1221.30084Gauthier, Paul M.; Clouâtre, Raphaël 3 2008 Luzin-type harmonic approximation on subsets of non-compact Riemannian manifolds. Zbl 1417.31005Gauthier, P. M.; Sharifi, F. 3 2019 Luzin-type holomorphic approximation on closed subsets of open Riemann surfaces. Zbl 1369.30039Gauthier, Paul M.; Sharifi, Fatemeh 3 2017 Complex approximation and extension-interpolation on arbitrary sets in one dimension. Zbl 1361.30059Gauthier, P. M. 3 2015 Conformal extensions of functions defined on arbitrary subsets of Riemann surfaces. Zbl 1310.30001Gauthier, P. M.; Nestoridis, V. 2 2015 Runge- and Walsh-type extensions of smooth subharmonic functions on open Riemann surfaces. Zbl 1314.31001Boivin, A.; Gauthier, P. M.; Paramonov, P. V. 2 2015 Non-extendable zero sets of harmonic and holomorphic functions. Zbl 1345.31012Gauthier, P. M. 2 2016 Tangential harmonic approximation on Riemannian manifolds. Zbl 0910.31005Bagby, Thomas; Gauthier, P. M.; Woodworth, Jennifer 2 1997 Complex approximation for vector-valued functions with an application to boundary behaviour. Zbl 0291.30018Brown, Leon; Gauthier, P. M.; Seidel, W. 2 1974 Interpolation in separable Frechet spaces with applications to spaces of analytic functions. Zbl 0322.46006Gauthier, Paul M.; Rubel, Lee A. 2 1975 Cercles de remplissage and asymptotic behaviour along circuitous paths. Zbl 0194.38102Gauthier, P. M. 2 1970 The value distribution of most functions of one or several complex variables. Zbl 0233.32001Gauthier, P. M.; Hengartner, Walter 2 1972 Degenerate cases of uniform approximation by solutions of systems with surjective symbols. Zbl 0795.35003Gauthier, P. M.; Tarkhanov, N. N. 2 1993 Approximation harmonique sur les surfaces de Riemann. Zbl 0509.31003Boivin, A.; Gauthier, P. M. 2 1984 Alice in Switzerland: the life and mathematics of Alice Roth. Zbl 1154.01316Daepp, Ulrich; Gauthier, Paul; Gorkin, Pamela; Schmieder, Gerald 2 2005 Universal (pluri)subharmonic functions. Zbl 1145.32016Gauthier, Paul M.; Pouryayevali, Mohamad R. 2 2007 From local to global properties of subharmonic functions on Green spaces. Zbl 0379.31006Gauthier, P. M.; Goldstein, M. 2 1977 The Carathéodory reflection principle and Osgood-Carathéodory theorem on Riemann surfaces. Zbl 1360.30010Gauthier, Paul M.; Sharifi, Fatemeh 2 2016 \(C^{m}\)-subharmonic extension of Runge type from closed to open subsets of \(\mathbb R^{N}\). Zbl 1298.31008Boivin, A.; Gauthier, P. M.; Paramonov, P. V. 2 2012 A maximum principle for subharmonic and plurisubharmonic functions. Zbl 0729.30025Chen, Huaihui; Gauthier, P. M. 2 1992 Uniform approximation on closed sets by solutions of elliptic partial differential equations. Zbl 0607.35032Dufresnoy, A.; Gauthier, P. M.; Ow, W. H. 1 1986 On tangential approximation by holomorphic functions. Zbl 0538.30035Arakelyan, N. U.; Gauthier, P. M. 1 1982 Approximation of a function and its derivatives by entire functions. Zbl 1338.30024Gauthier, Paul M.; Kienzle, Julie 1 2016 On the instability of the Riemann hypothesis for curves over finite fields. Zbl 1268.11086Gauthier, P. M.; Tarkhanov, N. 1 2012 Uniform approximation: Holomorphic, harmonic, subharmonic. Zbl 0839.30042Gauthier, P. M. 1 1994 Superharmonic approximation on the closed sets. Zbl 0835.31008Bensouda, Ch.; Gauthier, P. M. 1 1994 Fusion of two solutions of a partial differential equation. Zbl 0849.35013Blanchet, Pierre; Gauthier, Paul M. 1 1994 Propagation of smallness and uniqueness for harmonic and holomorphic functions. Zbl 0938.31002Arakelyan, N. U.; Gauthier, P. M. 1 1995 Uniform approximation and fine potential theory. Zbl 0782.31002Gauthier, P. M.; Ladouceur, S. 1 1993 Compact approximation by bounded functions and functions continuous up to the boundary. Zbl 1183.30032Gauthier, Paul M.; Melnikov, Mark S. 1 2009 Rational approximation and universality for a quasilinear parabolic equation. Zbl 1181.41020Gauthier, P. M.; Tarkhanov, N. 1 2008 Mini-workshop: Complex approximation and universality. Abstracts from the mini-workshop held February 10–16, 2008. Zbl 1177.30002 1 2008 Une application de la théorie de l’approximation à l’étude des fonctions holomorphes. Zbl 0261.30020Gauthier, P. M. 1 1973 Problème de surjectivite des applications holomorphes. Zbl 0278.32017Gauthier, P. M.; Ngo Van Que 1 1974 Équidistribution des valeurs d’une fonction analytique generique sur un espace de Stein. Zbl 0305.32012Brown, Leon; Gauthier, P. M. 1 1974 Approximation sur les fermes par des fonctions analytiques sur une surface de Riemann. Zbl 0322.30033Gauthier, P. M.; Hengartner, W. 1 1973 Harmonic approximation on compact sets. Zbl 1064.31006Bagby, Thomas; Gauthier, Paul M. 1 2003 Cercles de remplissage and asymptotic behaviour. Zbl 0181.35501Gauthier, P. 1 1969 The maximum modulus of normal meromorphic functions and applications to value distribution. Zbl 0202.36101Gauthier, P. 1 1970 The range set of a meromorphic function - a topological approach. Zbl 0215.13102Brown, L.; Gauthier, P. M. 1 1971 Best uniform approximation by harmonic functions on subsets of Riemannian manifolds. Zbl 0799.41025Gauthier, P. M.; Zwick, D. 1 1994 Cercles de remplissage for the Riemann zeta function. Zbl 1037.11056Gauthier, P. M. 1 2003 Selected papers. With brief biographical sketches by W. E. Sewell, D. V. Widder and Morris Marden and commentaries by Q. I. Rahman, P. M. Gauthier, Dieter Gaier, Walter Schempp and the editors. Edited by Theodore J. Rivlin and Edward B. Saff. Zbl 0971.01015Walsh, Joseph L. 1 2000 Carleman approximation on products of Riemann surfaces. Zbl 1054.32503Chacrone, Seddik; Gauthier, Paul M.; Nersessian, Ashot H. 1 1998 Normal functions: \(L^ p\) estimates. Zbl 0874.30027Chen, Huaihui; Gauthier, Paul M. 1 1997 A function algebra providing new Mergelyan type theorems in several complex variables. Zbl 1462.32002Falcó, Javier; Gauthier, Paul M.; Manolaki, Myrto; Nestoridis, Vassili 3 2021 An asymptotic holomorphic boundary problem on arbitrary open sets in Riemann surfaces. Zbl 1452.30020Falcó, Javier; Gauthier, Paul M. 1 2020 Luzin-type harmonic approximation on subsets of non-compact Riemannian manifolds. Zbl 1417.31005Gauthier, P. M.; Sharifi, F. 3 2019 Extendability and domains of holomorphy in infinite-dimensional spaces. Zbl 1439.46033Aron, Richard M.; Charpentier, Stéphane; Gauthier, Paul M.; Maestre, Manuel; Nestoridis, Vassili 1 2019 Approximation by solutions of elliptic equations and extension of subharmonic functions. Zbl 1412.30121Gauthier, Paul; Paramonov, Petr V. 1 2018 On zero sets of harmonic and real analytic functions. Zbl 1408.31003Boivin, André; Gauthier, Paul M.; Manolaki, Myrto 1 2018 Dirichlet approximation and universal Dirichlet series. Zbl 1386.30057Aron, Richard M.; Bayart, Frédéric; Gauthier, Paul M.; Maestre, Manuel; Nestoridis, Vassili 9 2017 Luzin-type holomorphic approximation on closed subsets of open Riemann surfaces. Zbl 1369.30039Gauthier, Paul M.; Sharifi, Fatemeh 3 2017 Uniform approximation in the spherical distance by functions meromorphic on Riemann surfaces. Zbl 1353.30043Gauthier, P. M.; Sharifi, F. 1 2017 Density of polynomials in classes of functions on products of planar domains. Zbl 1331.46044Gauthier, P. M.; Nestoridis, V. 6 2016 Non-extendable zero sets of harmonic and holomorphic functions. Zbl 1345.31012Gauthier, P. M. 2 2016 The Carathéodory reflection principle and Osgood-Carathéodory theorem on Riemann surfaces. Zbl 1360.30010Gauthier, Paul M.; Sharifi, Fatemeh 2 2016 Approximation of a function and its derivatives by entire functions. Zbl 1338.30024Gauthier, Paul M.; Kienzle, Julie 1 2016 Complex approximation and extension-interpolation on arbitrary sets in one dimension. Zbl 1361.30059Gauthier, P. M. 3 2015 Conformal extensions of functions defined on arbitrary subsets of Riemann surfaces. Zbl 1310.30001Gauthier, P. M.; Nestoridis, V. 2 2015 Runge- and Walsh-type extensions of smooth subharmonic functions on open Riemann surfaces. Zbl 1314.31001Boivin, A.; Gauthier, P. M.; Paramonov, P. V. 2 2015 Lectures on several complex variables. Zbl 1310.32001Gauthier, Paul M. 5 2014 Mergelyan’s theorem with polynomials non-vanishing on unions of sets. Zbl 1295.30087Andersson, J.; Gauthier, P. M. 3 2014 Universally overconvergent power series via the Riemann Zeta-function. Zbl 1281.30039Gauthier, P. M. 1 2013 Approximating the Riemann zeta-function by strongly recurrent functions. Zbl 1277.11085Gauthier, P. M. 1 2013 Approximating functions by the Riemann zeta-function and by polynomials with zero constraints. Zbl 1264.30023Gauthier, Paul M. 4 2012 Zero-free polynomial approximation on a chain of Jordan domains. Zbl 1293.30074Gauthier, Paul M.; Knese, Greg 4 2012 \(C^{m}\)-subharmonic extension of Runge type from closed to open subsets of \(\mathbb R^{N}\). Zbl 1298.31008Boivin, A.; Gauthier, P. M.; Paramonov, P. V. 2 2012 On the instability of the Riemann hypothesis for curves over finite fields. Zbl 1268.11086Gauthier, P. M.; Tarkhanov, N. 1 2012 The Landau theorem and Bloch theorem for planar harmonic and pluriharmonic mappings. Zbl 1234.30024Chen, Huaihui; Gauthier, Paul M. 17 2011 Approximation of and by the Riemann zeta-function. Zbl 1284.11122Gauthier, Paul M. 8 2010 Composition operators on \(\mu\)-Bloch spaces. Zbl 1171.47020Chen, Huaihui; Gauthier, Paul 19 2009 Perturbations of \(L\)-functions with or without non-trivial zeros off the critical line. Zbl 1250.11084Gauthier, Paul M.; Xarles, Xavier 3 2009 Compact approximation by bounded functions and functions continuous up to the boundary. Zbl 1183.30032Gauthier, Paul M.; Melnikov, Mark S. 1 2009 Boundedness from below of composition operators on \(\alpha\)-Bloch spaces. Zbl 1148.30017Chen, Huaihui; Gauthier, Paul 12 2008 Approximation by translates of Taylor polynomials of the Riemann zeta function. Zbl 1221.30084Gauthier, Paul M.; Clouâtre, Raphaël 3 2008 Rational approximation and universality for a quasilinear parabolic equation. Zbl 1181.41020Gauthier, P. M.; Tarkhanov, N. 1 2008 Mini-workshop: Complex approximation and universality. Abstracts from the mini-workshop held February 10–16, 2008. Zbl 1177.30002 1 2008 Weighted Hardy spaces for the unit disc: approximation properties. Zbl 1146.30034Boivin, André; Gauthier, Paul M.; Zhu, Changzhong 3 2007 Universal (pluri)subharmonic functions. Zbl 1145.32016Gauthier, Paul M.; Pouryayevali, Mohamad R. 2 2007 Universal overconvergence of homogeneous expansions of harmonic functions. Zbl 1132.31002Gauthier, Paul M.; Tamptse, Innocent 7 2006 Simultaneous approximation on two subsets of an open Riemann surface. Zbl 1096.30034Boivin, André; Gauthier, Paul M.; Schmieder, Gerald 1 2006 Approximation by the Riemann zeta-function. Zbl 1101.30038Gauthier, P. M.; Tarkhanov, N. 6 2005 The existence of universal inner functions on the unit ball of \(\mathbb C^n\). Zbl 1105.32003Gauthier, P. M.; Xiao, J. 6 2005 Alice in Switzerland: the life and mathematics of Alice Roth. Zbl 1154.01316Daepp, Ulrich; Gauthier, Paul; Gorkin, Pamela; Schmieder, Gerald 2 2005 Covering properties of most entire functions on Stein manifolds. Zbl 1090.32002Gauthier, Paul M.; Pouryayevali, Mohamad R. 1 2005 On uniform approximation by \(n\)-analytic functions on closed sets in \(\mathbb C\). Zbl 1069.30076Boivin, A.; Gauthier, P. M.; Paramonov, P. V. 11 2004 Small perturbations of the Riemann zeta function and their zeros. Zbl 1051.11046Gauthier, Paul M.; Zeron, Eduardo S. 5 2004 Failure of Landau’s theorem for quasiconformal mappings of the disc. Zbl 1074.30019Gauthier, P. M.; Pouryayevali, M. R. 4 2004 Harmonic approximation on compact sets. Zbl 1064.31006Bagby, Thomas; Gauthier, Paul M. 1 2003 Cercles de remplissage for the Riemann zeta function. Zbl 1037.11056Gauthier, P. M. 1 2003 BiBloch-type maps: existence and beyond. Zbl 1026.30035Gauthier, Paul M.; Xiao, Jie 12 2002 Approximation on closed sets by analytic or meromorphic solutions of elliptic equations and applications. Zbl 1022.30043Boivin, André; Gauthier, Paul M.; Paramonov, Petr V. 9 2002 Approximation on arcs and dendrites going to infinity in \(\mathbb{C}^n\). Zbl 1012.32003Gauthier, P. M.; Zeron, E. S. 6 2002 Bloch constants in several variables. Zbl 0966.32002Chen, Huaihui; Gauthier, P. M. 22 2001 Approximation by meromorphic functions with Mittag-Leffler type constraints. Zbl 0994.30022Gauthier, P. M.; Pouryayevali, M. R. 6 2001 Holomorphic and harmonic approximation on Riemann surfaces. Zbl 1017.30044Boivin, André; Gauthier, Paul M. 3 2001 Bloch constants for planar harmonic mappings. Zbl 0956.30012Chen, Huaihui; Gauthier, P. M.; Hengartner, W. 56 2000 Selected papers. With brief biographical sketches by W. E. Sewell, D. V. Widder and Morris Marden and commentaries by Q. I. Rahman, P. M. Gauthier, Dieter Gaier, Walter Schempp and the editors. Edited by Theodore J. Rivlin and Edward B. Saff. Zbl 0971.01015Walsh, Joseph L. 1 2000 Mittag-Leffler theorems on Riemann surfaces and Riemannian manifolds. Zbl 0914.30033Gauthier, Paul M. 3 1998 Carleman approximation on products of Riemann surfaces. Zbl 1054.32503Chacrone, Seddik; Gauthier, Paul M.; Nersessian, Ashot H. 1 1998 Tangential harmonic approximation on Riemannian manifolds. Zbl 0910.31005Bagby, Thomas; Gauthier, P. M.; Woodworth, Jennifer 2 1997 Normal functions: \(L^ p\) estimates. Zbl 0874.30027Chen, Huaihui; Gauthier, Paul M. 1 1997 On Bloch’s constant. Zbl 0864.30025Chen, Huaihui; Gauthier, Paul M. 19 1996 Recent developments in harmonic approximation, with applications. Zbl 0859.31001Armitage, D. H.; Gauthier, P. M. 10 1996 On strongly normal functions. Zbl 0879.30019Chen, Huaihui; Gauthier, Paul M. 3 1996 Propagation of smallness and uniqueness for harmonic and holomorphic functions. Zbl 0938.31002Arakelyan, N. U.; Gauthier, P. M. 1 1995 Subharmonic extensions and approximations. Zbl 0790.31001Gauthier, P. M. 11 1994 Uniform approximation. Zbl 0810.30001Gauthier, Paul M. 7 1994 Harmonic approximation on closed subsets of Riemannian manifolds. Zbl 0806.31003Bagby, Thomas; Gauthier, Paul M. 3 1994 Uniform approximation: Holomorphic, harmonic, subharmonic. Zbl 0839.30042Gauthier, P. M. 1 1994 Superharmonic approximation on the closed sets. Zbl 0835.31008Bensouda, Ch.; Gauthier, P. M. 1 1994 Fusion of two solutions of a partial differential equation. Zbl 0849.35013Blanchet, Pierre; Gauthier, Paul M. 1 1994 Best uniform approximation by harmonic functions on subsets of Riemannian manifolds. Zbl 0799.41025Gauthier, P. M.; Zwick, D. 1 1994 Degenerate cases of uniform approximation by solutions of systems with surjective symbols. Zbl 0795.35003Gauthier, P. M.; Tarkhanov, N. N. 2 1993 Uniform approximation and fine potential theory. Zbl 0782.31002Gauthier, P. M.; Ladouceur, S. 1 1993 Approximation by (pluri) subharmonic functions: Fusion and localization. Zbl 0782.31001Gauthier, P. M. 5 1992 Uniform approximation by global harmonic functions. Zbl 0759.41017Bagby, T.; Gauthier, P. M. 4 1992 A maximum principle for subharmonic and plurisubharmonic functions. Zbl 0729.30025Chen, Huaihui; Gauthier, P. M. 2 1992 Approximation by harmonic functions of closed subsets of Riemann surfaces. Zbl 0671.30037Bagby, Thomas; Gauthier, P. M. 9 1988 Approximation of a function and its derivatives by entire functions of several variables. Zbl 0641.32011Frih, El Mostapha; Gauthier, Paul M. 7 1988 Asymptotic maximum principles for subharmonic and plurisubharmonic functions. Zbl 0661.31007Gauthier, P. M.; Grothmann, R.; Hengartner, W. 7 1988 Uniform approximation on closed sets by solutions of elliptic partial differential equations. Zbl 0569.35022Dufresnoy, A.; Gauthier, P. M.; Ow, W. H. 4 1986 Uniform approximation on closed sets by solutions of elliptic partial differential equations. Zbl 0607.35032Dufresnoy, A.; Gauthier, P. M.; Ow, W. H. 1 1986 Global holomorphic approximations of CR functions on CR manifolds. Zbl 0548.32011Dwilewicz, Roman; Gauthier, P. M. 3 1985 Note on the decay of solutions of elliptic equations. Zbl 0563.35028Armitage, D. H.; Bagby, Thomas; Gauthier, P. M. 3 1985 Approximation harmonique sur les surfaces de Riemann. Zbl 0509.31003Boivin, A.; Gauthier, P. M. 2 1984 Uniform approximation on closed sets by harmonic functions with Newtonian singularities. Zbl 0525.31002Gauthier, P. M.; Goldstein, M.; Ow, W. H. 9 1983 Approximation uniforme qualitative sur des ensembles non bornes. Zbl 0482.30028Gauthier, Paul M.; Hengartner, Walter 5 1982 On tangential approximation by holomorphic functions. Zbl 0538.30035Arakelyan, N. U.; Gauthier, P. M. 1 1982 Uniform approximation on unbounded sets by harmonic functions with logarithmic singularities. Zbl 0447.30035Gauthier, P. M.; Goldstein, M.; Ow, W. H. 9 1980 Meromorphic uniform approximation on closed subsets of open Riemann surfaces. Zbl 0409.30033Gauthier, P. M. 4 1979 Complex approximation and simultaneous interpolation on closed sets. Zbl 0338.30026Gauthier, P. M.; Hengartner, W. 6 1977 From local to global properties of subharmonic functions on Green spaces. Zbl 0379.31006Gauthier, P. M.; Goldstein, M. 2 1977 On the possibility of rational approximation. Zbl 0386.41009Gauthier, P. M. 1 1977 Possibility of uniform rational approximation in the spherical metric. Zbl 0322.30036Gauthier, P. M.; Roth, A.; Walsh, Joseph L. 6 1976 Holomorphic functionals on open Riemann surfaces. Zbl 0321.46032Gauthier, P. M.; Rubel, L. A. 3 1976 The set of Julia points for functions omitting two values. Zbl 0369.30024Gauthier, P. M.; Hwang, J. S. 1 1976 Continuous boundary behaviour for functions defined in the open unit disc. Zbl 0307.30031Brown, Leon; Gauthier, P. M.; Hengartner, Walter 7 1975 Uniform approximation on closed sets by functions analytic on a Riemann surface. Zbl 0322.30034Gauthier, P. M.; Hengartner, W. 6 1975 Interpolation in separable Frechet spaces with applications to spaces of analytic functions. Zbl 0322.46006Gauthier, Paul M.; Rubel, Lee A. 2 1975 Complex approximation for vector-valued functions with an application to boundary behaviour. Zbl 0291.30018Brown, Leon; Gauthier, P. M.; Seidel, W. 2 1974 Problème de surjectivite des applications holomorphes. Zbl 0278.32017Gauthier, P. M.; Ngo Van Que 1 1974 Équidistribution des valeurs d’une fonction analytique generique sur un espace de Stein. Zbl 0305.32012Brown, Leon; Gauthier, P. M. 1 1974 Local harmonic majorants of functions subharmonic in the unit disc. Zbl 0279.31001Gauthier, P. M.; Hengartner, Walter 9 1973 ...and 11 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 324 Authors 45 Gauthier, Paul M. 18 Chen, Shaolin 17 Ponnusamy, Saminathan 14 Liu, Mingsheng 14 Nestoridis, Vassili 13 Wang, Xiantao 12 Chen, Huaihui 9 Gardiner, Stephen J. 7 Zhang, Xuejun 6 Boivin, André 6 Maestre, Manuel 6 Manolaki, Myrto 5 Bernal-Gonzàlez, Luis 5 Falcó, Javier 5 Hamada, Hidetaka 4 Abdulhadi, Zayid 4 Aulaskari, Rauno 4 Bagby, Thomas 4 Bayart, Frédéric 4 Burke, Maxim R. 4 Dai, Jineng 4 Doubtsov, Evgueni Sergeevich 4 Gorkin, Pamela B. 4 Kohr, Gabriela 4 Li, Shenlian 4 Paramonov, Peter V. 4 Stević, Stevo 4 Wold, Erlend Fornæss 4 Xu, Si 4 Zorboska, Nina 3 Armitage, David H. 3 Boggess, Albert 3 Brown, Leon 3 Calderón-Moreno, María del Carmen 3 Carmona, Joan Josep 3 Charpentier, Stéphane 3 Danielyan, Arthur A. 3 Dwilewicz, Roman J. 3 Fedorovskiĭ, K. Yu. 3 Fedorovskiy, Konstantin Yu. 3 García, Domingo 3 Goldstein, Myron 3 Hed, Lisa 3 Kalaj, David 3 Kayumov, Il’giz Rifatovich 3 Lappan, Peter A. 3 Li, Peijin 3 Li, Songxiao 3 Liu, Taishun 3 Mashreghi, Javad 3 Nieß, Markus 3 Prado-Bassas, José Antonio 3 Rasila, Antti 3 Schmieder, Gerald 3 Sharifi, Fatemeh 3 Wang, Jianfei 3 Zhu, Jianfeng 2 Abakumov, Evgeny V. 2 Abu-Muhanna, Yusuf 2 Ali, Rosihan Mohamed 2 Aron, Richard Martin 2 Baranov, Anton D. 2 Bisi, Cinzia 2 Blanchet, Pierre 2 Bonilla, Antonio 2 Castillo-Medina, Jaime 2 Efraimidis, Iason 2 Enciso, Alberto 2 Fariña, Juan Carlos 2 Golitsyna, Mayya 2 Grosse-Erdmann, Karl-Goswin 2 Khavin, Viktor Petrovich 2 Hengartner, Walter 2 Hernández, Rodrigo 2 Honda, Tatsuhiro 2 Jupiter, Daniel C. 2 Kanas, Stanisława R. 2 Khabibullin, Bulat Nurmievich 2 Khalfallah, Adel 2 Kobayashi, Shoji 2 Liu, Zhenxing 2 Luo, Lifang 2 Luo, Xi 2 Maharana, Sudhananda 2 Mhamdi, Mohamed 2 Mortini, Raymond 2 Nikolov, Nikolai Marinov 2 Ow, Wellington Ham 2 Pavićević, Žarko 2 Peralta-Salas, Daniel 2 Persson, Hakan 2 Pflug, Peter 2 Pouryayevali, Mohamad Reza 2 Ramos-Fernández, Julio C. 2 Schippers, Eric D. 2 Sevilla-Peris, Pablo 2 Starkov, Victor V. 2 Staubach, Wolfgang 2 Tarkhanov, Nikolai N. 2 Veronelli, Giona ...and 224 more Authors all top 5 Cited in 110 Serials 33 Journal of Mathematical Analysis and Applications 20 Computational Methods and Function Theory 18 Complex Variables and Elliptic Equations 15 Journal of Approximation Theory 14 Journal d’Analyse Mathématique 14 Proceedings of the American Mathematical Society 13 Monatshefte für Mathematik 13 Complex Analysis and Operator Theory 11 Transactions of the American Mathematical Society 7 Mathematische Annalen 5 Nagoya Mathematical Journal 5 The Journal of Geometric Analysis 5 Proceedings of the Steklov Institute of Mathematics 5 Analysis and Mathematical Physics 4 Applied Mathematics and Computation 4 Science in China. 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Second Series 1 Communications of the Korean Mathematical Society 1 Lobachevskii Journal of Mathematics ...and 10 more Serials all top 5 Cited in 30 Fields 208 Functions of a complex variable (30-XX) 99 Potential theory (31-XX) 82 Several complex variables and analytic spaces (32-XX) 46 Operator theory (47-XX) 37 Functional analysis (46-XX) 27 Approximations and expansions (41-XX) 22 Partial differential equations (35-XX) 17 Number theory (11-XX) 5 Real functions (26-XX) 4 Global analysis, analysis on manifolds (58-XX) 3 Mathematical logic and foundations (03-XX) 2 History and biography (01-XX) 2 Dynamical systems and ergodic theory (37-XX) 2 Harmonic analysis on Euclidean spaces (42-XX) 2 Differential geometry (53-XX) 2 General topology (54-XX) 2 Probability theory and stochastic processes (60-XX) 2 Numerical analysis (65-XX) 2 Fluid mechanics (76-XX) 1 Group theory and generalizations (20-XX) 1 Ordinary differential equations (34-XX) 1 Sequences, series, summability (40-XX) 1 Abstract harmonic analysis (43-XX) 1 Calculus of variations and optimal control; optimization (49-XX) 1 Geometry (51-XX) 1 Manifolds and cell complexes (57-XX) 1 Mechanics of deformable solids (74-XX) 1 Quantum theory (81-XX) 1 Game theory, economics, finance, and other social and behavioral sciences (91-XX) 1 Systems theory; control (93-XX) Citations by Year