Guillemin, Victor W.; Uribe, Alejandro; Wang, Zuoqin Integral representations of isotropic semiclassical functions and applications. (English) Zbl 1487.58026 J. Spectr. Theory 12, No. 1, 227-258 (2022). Reviewer: Antonio Roberto da Silva (Rio de Janeiro) MSC: 58J40 58C35 81Q20 PDFBibTeX XMLCite \textit{V. W. Guillemin} et al., J. Spectr. Theory 12, No. 1, 227--258 (2022; Zbl 1487.58026) Full Text: DOI arXiv
Guillemin, V.; Uribe, A.; Wang, Z. Spectral properties of semi-classical Toeplitz operators. (English) Zbl 1418.58009 Kac, Victor G. (ed.) et al., Lie groups, geometry, and representation theory. A tribute to the life and work of Bertram Kostant. Cham: Birkhäuser. Prog. Math. 326, 185-199 (2018). Reviewer: Emilio A. Lauret (Córdoba) MSC: 58J50 47B35 81Q20 58J53 PDFBibTeX XMLCite \textit{V. Guillemin} et al., Prog. Math. 326, 185--199 (2018; Zbl 1418.58009) Full Text: DOI arXiv
Boutet de Monvel, Louis Guillemin, Victor W. (ed.); Sjöstrand, Johannes (ed.) Selected works. Edited by Victor W. Guillemin and Johannes Sjöstrand. (English) Zbl 1379.35002 Contemporary Mathematicians. Basel: Birkhäuser/Springer (ISBN 978-3-319-27907-7/hbk; 978-3-319-27909-1/ebook). vii, 852 p. (2017). MSC: 35-03 47-03 32-03 01A75 01A70 01A60 35A27 35Sxx PDFBibTeX XMLCite \textit{L. Boutet de Monvel} et al., Selected works. Edited by Victor W. Guillemin and Johannes Sjöstrand. Basel: Birkhäuser/Springer (2017; Zbl 1379.35002) Full Text: DOI
Guillemin, V.; Uribe, A.; Wang, Z. Semiclassical states associated with isotropic submanifolds of phase space. (English) Zbl 1362.58014 Lett. Math. Phys. 106, No. 12, 1695-1728 (2016). Reviewer: Luigi Rodino (Torino) MSC: 58J40 81Q20 35S05 PDFBibTeX XMLCite \textit{V. Guillemin} et al., Lett. Math. Phys. 106, No. 12, 1695--1728 (2016; Zbl 1362.58014) Full Text: DOI arXiv Link
Guillemin, Victor; Sternberg, Shlomo Semi-classical analysis. (English) Zbl 1298.58001 Somerville, MA: International Press (ISBN 978-1-57146-276-3/pbk). xxiv, 446 p. (2013). Reviewer: Sönke Hansen (Paderborn) MSC: 58-02 58J40 58J50 35S99 53D05 81Q20 81Q10 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{S. Sternberg}, Semi-classical analysis. Somerville, MA: International Press (2013; Zbl 1298.58001)
Colin de Verdière, Yves; Guillemin, Victor A semi-classical inverse problem. I: Taylor expansions. (English) Zbl 1258.34036 van den Ban, Erik P. (ed.) et al., Geometric aspects of analysis and mechanics. In honor of the 65th birthday of Hans Duistermaat. Basel: Birkhäuser (ISBN 978-0-8176-8243-9/hbk; 978-0-8176-8244-6/ebook). Progress in Mathematics 292, 81-95 (2011). Reviewer: Alexey Fedoseev (Saratov) MSC: 34A55 34L40 34E20 81Q10 81Q20 47G30 PDFBibTeX XMLCite \textit{Y. Colin de Verdière} and \textit{V. Guillemin}, Prog. Math. 292, 81--95 (2011; Zbl 1258.34036) Full Text: DOI arXiv
Guillemin, Victor; Paul, Thierry Some remarks about semiclassical trace invariants and quantum normal forms. (English) Zbl 1213.58021 Commun. Math. Phys. 294, No. 1, 1-19 (2010). Reviewer: Peter B. Gilkey (Eugene) MSC: 58J50 58J40 81Q20 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{T. Paul}, Commun. Math. Phys. 294, No. 1, 1--19 (2010; Zbl 1213.58021) Full Text: DOI arXiv
Friedlander, Leonid; Guillemin, Victor Determinants of zeroth order operators. (English) Zbl 1140.58017 J. Differ. Geom. 78, No. 1, 1-12 (2008). MSC: 58J52 58J40 PDFBibTeX XMLCite \textit{L. Friedlander} and \textit{V. Guillemin}, J. Differ. Geom. 78, No. 1, 1--12 (2008; Zbl 1140.58017) Full Text: DOI arXiv Euclid
Guillemin, V.; Paul, T.; Uribe, A. “Bottom of the well” semi-classical trace invariants. (English) Zbl 1140.58007 Math. Res. Lett. 14, No. 4, 711-719 (2007). MSC: 58J40 58J37 PDFBibTeX XMLCite \textit{V. Guillemin} et al., Math. Res. Lett. 14, No. 4, 711--719 (2007; Zbl 1140.58007) Full Text: DOI arXiv
Guillemin, Victor; Uribe, Alejandro Some inverse spectral results for semi-classical Schrödinger operators. (English) Zbl 1138.35006 Math. Res. Lett. 14, No. 4, 623-632 (2007). MSC: 35J10 35S05 47G30 81Q20 81U40 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{A. Uribe}, Math. Res. Lett. 14, No. 4, 623--632 (2007; Zbl 1138.35006) Full Text: DOI arXiv
Guillemin, V.; Lerman, E. Melrose-Uhlmann projectors, the metaplectic representation and symplectic cuts. (English) Zbl 1071.53540 J. Differ. Geom. 61, No. 3, 365-396 (2002). MSC: 53D20 58J40 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{E. Lerman}, J. Differ. Geom. 61, No. 3, 365--396 (2002; Zbl 1071.53540) Full Text: DOI arXiv
Guillemin, Victor Paley-Wiener on manifolds. (English) Zbl 0916.58043 Jerison, David (ed.) et al., The legacy of Norbert Wiener: a centennial symposium. In honor of the 100th anniversary of Norbert Wiener’s birth, October 8-14, 1994, Cambridge, MA, USA. Providence, RI: American Mathematical Society. Proc. Symp. Pure Math. 60, 85-91 (1997). Reviewer: M.Marvan (Opava) MSC: 58J40 42B10 32C05 PDFBibTeX XMLCite \textit{V. Guillemin}, Proc. Symp. Pure Math. 60, 85--91 (1997; Zbl 0916.58043)
Guillemin, V.; Okikiolu, K. Subprincipal terms in Szegö estimates. (English) Zbl 0881.58064 Math. Res. Lett. 4, No. 1, 173-179 (1997). Reviewer: B.Helffer (Orsay) MSC: 58J40 35P20 58J50 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{K. Okikiolu}, Math. Res. Lett. 4, No. 1, 173--179 (1997; Zbl 0881.58064) Full Text: DOI
Guillemin, V.; Okikiolu, K. Szegö theorems for Zoll operators. (English) Zbl 0899.47038 Math. Res. Lett. 3, No. 4, 449-452 (1996). Reviewer: B.Rubin (Jerusalem) MSC: 47G30 47B38 35S05 58C40 35P20 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{K. Okikiolu}, Math. Res. Lett. 3, No. 4, 449--452 (1996; Zbl 0899.47038) Full Text: DOI
Guillemin, Victor Wave-trace invariants. (English) Zbl 0858.58051 Duke Math. J. 83, No. 2, 287-352 (1996). Reviewer: G.E.Karadzhov (Sofia) MSC: 58J50 58J40 PDFBibTeX XMLCite \textit{V. Guillemin}, Duke Math. J. 83, No. 2, 287--352 (1996; Zbl 0858.58051) Full Text: DOI
Brüning, Jochen (ed.); Guillemin, Victor W. (ed.) Mathematics past and present. Fourier integral operators. Selected classical articles by J. J. Duistermaat, V. W. Guillemin and L. Hörmander. (English) Zbl 0791.47043 Berlin: Springer-Verlag. vii, 283 p. (1994). Reviewer: J.F.Toland (Bath) MSC: 47G20 35S30 47G30 01A75 58J40 78A40 PDFBibTeX XMLCite \textit{J. Brüning} (ed.) and \textit{V. W. Guillemin} (ed.), Mathematics past and present. Fourier integral operators. Selected classical articles by J. J. Duistermaat, V. W. Guillemin and L. Hörmander. Berlin: Springer-Verlag (1994; Zbl 0791.47043)
Guillemin, Victor Wave-trace invariants and a theorem of Zelditch. (English) Zbl 0798.58073 Int. Math. Res. Not. 1993, No. 12, 303-308 (1993). Reviewer: N.Jacob (Erlangen) MSC: 58J40 35S35 PDFBibTeX XMLCite \textit{V. Guillemin}, Int. Math. Res. Not. 1993, No. 12, 303--308 (1993; Zbl 0798.58073) Full Text: DOI
Guillemin, Victor Gauged Lagrangian distributions. (English) Zbl 0803.58052 Adv. Math. 102, No. 2, 184-201 (1993). Reviewer: V.Oproiu (Iaşi) MSC: 58J40 37J99 PDFBibTeX XMLCite \textit{V. Guillemin}, Adv. Math. 102, No. 2, 184--201 (1993; Zbl 0803.58052) Full Text: DOI
Guillemin, Victor; Stenzel, Matthew Grauert tubes and the homogeneous Monge-Ampère equation. II. (English) Zbl 0789.32010 J. Differ. Geom. 35, No. 3, 627-641 (1992). Reviewer: S.Dimiev (Sofia) MSC: 32W20 58J40 58J05 53C20 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{M. Stenzel}, J. Differ. Geom. 35, No. 3, 627--641 (1992; Zbl 0789.32010) Full Text: DOI
Guillemin, Victor; Uribe, Alejandro Reduction and the trace formula. (English) Zbl 0721.58050 J. Differ. Geom. 32, No. 2, 315-347 (1990). Reviewer: G.E.Karadzhov (Sofia) MSC: 58J50 58J70 47G30 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{A. Uribe}, J. Differ. Geom. 32, No. 2, 315--347 (1990; Zbl 0721.58050) Full Text: DOI
Guillemin, V.; Uribe, A. Some spectral properties of periodic potentials. (English) Zbl 0651.35067 Pseudo-differential operators, Proc. Conf., Oberwolfach/Ger. 1986, Lect. Notes Math. 1256, 192-213 (1987). Reviewer: S.K.Chatterjea MSC: 35P05 35S05 PDFBibTeX XML
Guillemin, Victor; Uribe, Alejandro Reduction, the trace formula, and semiclassical asymptotics. (English) Zbl 0639.58028 Proc. Natl. Acad. Sci. USA 84, 7799-7801 (1987). Reviewer: K.Furutani MSC: 58J40 58J50 81Q05 37J99 53D50 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{A. Uribe}, Proc. Natl. Acad. Sci. USA 84, 7799--7801 (1987; Zbl 0639.58028) Full Text: DOI
Guillemin, Victor On some results of Gelfand in integral geometry. (English) Zbl 0576.58028 Pseudodifferential operators and applications, Proc. Symp., Notre Dame/Indiana 1984, Proc. Symp. Pure Math. 43, 149-155 (1985). Reviewer: K.Furutani MSC: 58J40 53C65 PDFBibTeX XML
Guillemin, Victor A new proof of Weyl’s formula on the asymptotic distribution of eigenvalues. (English) Zbl 0559.58025 Adv. Math. 55, 131-160 (1985). Reviewer: N.Jacob MSC: 58J50 81S99 35P20 58J40 53D50 PDFBibTeX XMLCite \textit{V. Guillemin}, Adv. Math. 55, 131--160 (1985; Zbl 0559.58025) Full Text: DOI
Guillemin, Victor Toeplitz operators in \(n\)-dimensions. (English) Zbl 0561.47025 Integral Equations Oper. Theory 7, 145-205 (1984). Reviewer: W.Jarczyk MSC: 47B35 58J40 35S05 PDFBibTeX XMLCite \textit{V. Guillemin}, Integral Equations Oper. Theory 7, 145--205 (1984; Zbl 0561.47025) Full Text: DOI
Guillemin, V.; Sternberg, S. Homogeneous quantization and multiplicities of group representations. (English) Zbl 0733.58021 J. Funct. Anal. 47, No. 3, 344-380 (1982). MSC: 53D50 22E45 58J40 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{S. Sternberg}, J. Funct. Anal. 47, 344--380 (1982; Zbl 0733.58021) Full Text: DOI
Guillemin, V.; Sternberg, Sh. Geometric asymptotics. (Geometricheskie asimptotiki). Transl. from the English and with a preface by S. G. Gindikin. (Russian) Zbl 0498.58003 Moskva: ”Mir”. 502 p. R. 2.20 (1981). MSC: 58-02 53-02 37J99 35B40 44A99 53C15 58J99 58J35 58J40 58J50 53D50 22E27 78A05 58J45 58J47 53C80 PDFBibTeX XML
Guillemin, Victor Band asymptotics in two dimensions. (English) Zbl 0478.58029 Adv. Math. 42, 248-282 (1981). MSC: 58J50 58J40 53C20 58C40 35S05 35P15 35P20 PDFBibTeX XMLCite \textit{V. Guillemin}, Adv. Math. 42, 248--282 (1981; Zbl 0478.58029) Full Text: DOI
Guillemin, V.; Sternberg, S. The metaplectic representation, Weyl operators and spectral theory. (English) Zbl 0469.58017 J. Funct. Anal. 42, 128-225 (1981). MSC: 58J40 58J50 35P20 22D12 35S99 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{S. Sternberg}, J. Funct. Anal. 42, 128--225 (1981; Zbl 0469.58017) Full Text: DOI
Boutet de Monvel, L.; Guillemin, V. The spectral theory of Toeplitz operators. (English) Zbl 0469.47021 Annals of Mathematics Studies, No. 99. Princeton, New Jersey: Princeton University Press; University of Tokyo Press. V, 160 p. hbk: $ 23.00; pbk: $ 9.25 (1981). MSC: 47B35 35S99 32A35 47A10 42B10 47Gxx PDFBibTeX XML Full Text: DOI
Guillemin, V.; Uhlmann, G. Oscillatory integrals with singular symbols. (English) Zbl 0462.58030 Duke Math. J. 48, 251-267 (1981). MSC: 58J40 53C65 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{G. Uhlmann}, Duke Math. J. 48, 251--267 (1981; Zbl 0462.58030) Full Text: DOI
Guillemin, V.; Sternberg, S. The metaplectic representation, Weyl operators and spectral theory. (English) Zbl 0457.58018 Differential geometrical methods in mathematical physics, Proc. Conf. Aix-en-Provence and Salamanca 1979, Lect. Notes Math. 836, 420-431 (1980). MSC: 58J10 58J50 22E30 47Gxx PDFBibTeX XML
Guillemin, V.; Sternberg, S. On the spectra of commuting pseudodifferential operators: Recent work of Kac-Spencer, Weinstein and others. (English) Zbl 0502.58036 Partial differential equations and geometry, Proc. Park City Conf. 1977, Lect. Notes Pure Appl. Math. 48, 149-165 (1979). MSC: 58J50 47F05 58C40 PDFBibTeX XML
Guillemin, Victor; Sternberg, Shlomo Some problems in integral geometry and some related problems in micro- local analysis. (English) Zbl 0446.58019 Am. J. Math. 101, 915-955 (1979). MSC: 58J50 53C65 47Gxx 35P20 53D50 35A22 58J40 44A99 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{S. Sternberg}, Am. J. Math. 101, 915--955 (1979; Zbl 0446.58019) Full Text: DOI
Guillemin, Victor Some micro-local aspects of analysis on compact symmetric spaces. (English) Zbl 0425.58020 Semin. on micro-local analysis, Inst. adv. Study, Princeton/ New Jersey 1977-78, Ann. Math. Stud. 93, 79-111 (1979). MSC: 58J50 58J40 58J10 22E46 PDFBibTeX XML
Guillemin, Victor; Melrose, Richard The Poisson summation formula for manifolds with boundary. (English) Zbl 0421.35082 Adv. Math. 32, 204-232 (1979). MSC: 35S05 35J05 58J40 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{R. Melrose}, Adv. Math. 32, 204--232 (1979; Zbl 0421.35082) Full Text: DOI
Guillemin, Victor Lectures on spectral theory of elliptic operators. (English) Zbl 0463.58024 Duke Math. J. 44, 485-517 (1977). MSC: 58J40 58J50 53D50 PDFBibTeX XMLCite \textit{V. Guillemin}, Duke Math. J. 44, 485--517 (1977; Zbl 0463.58024) Full Text: DOI
Guillemin, Victor Lectures on spectral theory of elliptic operators. (English) Zbl 0447.58033 Duke Math. J. 44, 485-517 (1977). MSC: 58J50 58J10 53D50 70H99 58J40 37G99 22E46 43A80 PDFBibTeX XMLCite \textit{V. Guillemin}, Duke Math. J. 44, 485--517 (1977; Zbl 0447.58033) Full Text: DOI
Guillemin, Victor; Schaeffer, David On a certain class of Fuchsian partial differential equations. (English) Zbl 0356.35080 Duke Math. J. 44, 157-199 (1977). MSC: 35S05 35B99 PDFBibTeX XMLCite \textit{V. Guillemin} and \textit{D. Schaeffer}, Duke Math. J. 44, 157--199 (1977; Zbl 0356.35080) Full Text: DOI
Guillemin, Victor W. Symplectic spinors and partial differential equations. (English) Zbl 0341.58014 Geom. sympl. Phys. math., Colloq. int. Aix-en-Provence 1974, 217-252 (1975). MSC: 58J40 47Gxx 58A30 PDFBibTeX XML
Duistermaat, J. J.; Guillemin, V. W. The spectrum of positive elliptic operators and periodic geodesics. (English) Zbl 0322.35071 Differ. Geom., Proc. Symp. Pure Math. 27, Part 2, Stanford 1973, 205-209 (1975). MSC: 35P20 35S15 58J40 PDFBibTeX XML
Guillemin, V.; Schaeffer, D. Fourier integral operators from the Radon transform point of view. (English) Zbl 0313.46036 Differ. Geom., Proc. Symp. Pure Math. 27, Part 2, Stanford 1973, 297-300 (1975). MSC: 46F10 47Gxx 58J40 PDFBibTeX XML
Duistermaat, J. J.; Guillemin, V. W. The spectrum of positive elliptic operators and periodic bicharacteristics. (English) Zbl 0307.35071 Invent. Math. 29, 39-79 (1975). MSC: 35P20 58J40 PDFBibTeX XMLCite \textit{J. J. Duistermaat} and \textit{V. W. Guillemin}, Invent. Math. 29, 39--79 (1975; Zbl 0307.35071) Full Text: DOI EuDML