Boggess, Albert; Raich, Andrew The fundamental solution to \(\Box_b\) on quadric manifolds with nonzero eigenvalues and null variables. (English) Zbl 07818422 Pac. J. Math. 327, No. 2, 233-266 (2023). MSC: 32V20 32W10 35R03 42B37 43A80 PDFBibTeX XMLCite \textit{A. Boggess} and \textit{A. Raich}, Pac. J. Math. 327, No. 2, 233--266 (2023; Zbl 07818422) Full Text: DOI
Garofalo, Nicola; Tralli, Giulio Heat kernels for a class of hybrid evolution equations. (English) Zbl 1521.35099 Potential Anal. 59, No. 2, 823-856 (2023). MSC: 35K08 35R03 53C17 PDFBibTeX XMLCite \textit{N. Garofalo} and \textit{G. Tralli}, Potential Anal. 59, No. 2, 823--856 (2023; Zbl 1521.35099) Full Text: DOI arXiv
Boggess, Albert; Raich, Andrew The fundamental solution to \(\Box_b\) on quadric manifolds with nonzero eigenvalues. (English) Zbl 1517.32120 Trans. Am. Math. Soc., Ser. B 10, 507-541 (2023). MSC: 32W10 32V20 PDFBibTeX XMLCite \textit{A. Boggess} and \textit{A. Raich}, Trans. Am. Math. Soc., Ser. B 10, 507--541 (2023; Zbl 1517.32120) Full Text: DOI arXiv
Rottensteiner, David; Ruzhansky, Michael An update on the \(L^p\)-\(L^q\) norms of spectral multipliers on unimodular Lie groups. (English) Zbl 1522.43002 Arch. Math. 120, No. 5, 507-520 (2023). MSC: 43A15 35P15 22E30 PDFBibTeX XMLCite \textit{D. Rottensteiner} and \textit{M. Ruzhansky}, Arch. Math. 120, No. 5, 507--520 (2023; Zbl 1522.43002) Full Text: DOI arXiv
Lin, Qingze Gradient estimates for Schrödinger operators with characterizations of \(\mathrm{BMO}_{\mathcal{L}}\) on Heisenberg groups. (English) Zbl 1516.35205 Proc. Am. Math. Soc. 151, No. 5, 2127-2142 (2023). Reviewer: Denis A. White (Toledo) MSC: 35J10 35K08 43A80 PDFBibTeX XMLCite \textit{Q. Lin}, Proc. Am. Math. Soc. 151, No. 5, 2127--2142 (2023; Zbl 1516.35205) Full Text: DOI
Bogdan, Krzystzof (ed.); Kohatsu-Higa, Arturo (ed.); Ros-Oton, Xavier (ed.); Schilling, René (ed.) MFO-RIMS tandem workshop: Nonlocality in analysis, probability and statistics. Abstracts from the MFO-RIMS tandem workshop held March 20–26, 2022. (English) Zbl 1506.00046 Oberwolfach Rep. 19, No. 1, 709-815 (2022). MSC: 00B05 00B25 35-06 60-06 62-06 PDFBibTeX XMLCite \textit{K. Bogdan} (ed.) et al., Oberwolfach Rep. 19, No. 1, 709--815 (2022; Zbl 1506.00046) Full Text: DOI
Boggess, Albert; Raich, Andrew Analysis on quadrics. (English) Zbl 1504.32095 Complex Anal. Synerg. 8, No. 4, Paper No. 18, 18 p. (2022). MSC: 32V20 32W10 PDFBibTeX XMLCite \textit{A. Boggess} and \textit{A. Raich}, Complex Anal. Synerg. 8, No. 4, Paper No. 18, 18 p. (2022; Zbl 1504.32095) Full Text: DOI
Yang, Zhi Peng A note on the heat kernel for the rescaled harmonic oscillator from two step nilpotent Lie groups. (English) Zbl 1518.22013 Acta Math. Sin., Engl. Ser. 38, No. 9, 1597-1611 (2022). MSC: 22E25 43A75 35A08 PDFBibTeX XMLCite \textit{Z. P. Yang}, Acta Math. Sin., Engl. Ser. 38, No. 9, 1597--1611 (2022; Zbl 1518.22013) Full Text: DOI
Boggess, Albert; Raich, Andrew The fundamental solution to \(\Box_b\) on quadric manifolds. I: General formulas. (English) Zbl 1487.32201 Proc. Am. Math. Soc., Ser. B 9, 186-203 (2022). MSC: 32W10 35R03 32A25 PDFBibTeX XMLCite \textit{A. Boggess} and \textit{A. Raich}, Proc. Am. Math. Soc., Ser. B 9, 186--203 (2022; Zbl 1487.32201) Full Text: DOI arXiv
Li, Hong-Quan; Sjögren, Peter Estimates for operators related to the sub-Laplacian with drift in Heisenberg groups. (English) Zbl 1485.58022 J. Fourier Anal. Appl. 28, No. 1, Paper No. 10, 29 p. (2022). Reviewer: Daniel Beltiţă (Bucureşti) MSC: 58J35 22E25 43A80 58C35 PDFBibTeX XMLCite \textit{H.-Q. Li} and \textit{P. Sjögren}, J. Fourier Anal. Appl. 28, No. 1, Paper No. 10, 29 p. (2022; Zbl 1485.58022) Full Text: DOI
Boggess, Albert; Raich, Andrew The fundamental solution to \(\Box_b\) on quadric manifolds. III: Asymptotics for a codimension 2 case in \({\mathbb{C}}^4\). (English) Zbl 1482.32031 J. Geom. Anal. 31, No. 11, 11529-11583 (2021). Reviewer: Yunus E. Zeytuncu (Ann Arbor) MSC: 32W10 35R03 32V20 42B37 43A80 PDFBibTeX XMLCite \textit{A. Boggess} and \textit{A. Raich}, J. Geom. Anal. 31, No. 11, 11529--11583 (2021; Zbl 1482.32031) Full Text: DOI
Fernández-Bertolin, Aingeru; Jaming, Philippe; Pérez-Esteva, Salvador An uncertainty principle for solutions of the Schrödinger equation on \(H\)-type groups. (English) Zbl 1493.22007 J. Aust. Math. Soc. 111, No. 1, 1-16 (2021). Reviewer: Lubomira Softova (Salerno) MSC: 22E30 43A80 35K08 PDFBibTeX XMLCite \textit{A. Fernández-Bertolin} et al., J. Aust. Math. Soc. 111, No. 1, 1--16 (2021; Zbl 1493.22007) Full Text: DOI arXiv
Georgiev, Vladimir; Palmieri, Alessandro Lifespan estimates for local in time solutions to the semilinear heat equation on the Heisenberg group. (English) Zbl 1461.35129 Ann. Mat. Pura Appl. (4) 200, No. 3, 999-1032 (2021). MSC: 35K58 35B33 35B44 35R03 35K08 PDFBibTeX XMLCite \textit{V. Georgiev} and \textit{A. Palmieri}, Ann. Mat. Pura Appl. (4) 200, No. 3, 999--1032 (2021; Zbl 1461.35129) Full Text: DOI arXiv
Garofalo, Nicola; Tralli, Giulio Feeling the heat in a group of Heisenberg type. (English) Zbl 1459.35226 Adv. Math. 381, Article ID 107635, 43 p. (2021). MSC: 35K08 35R03 35R11 53C18 PDFBibTeX XMLCite \textit{N. Garofalo} and \textit{G. Tralli}, Adv. Math. 381, Article ID 107635, 43 p. (2021; Zbl 1459.35226) Full Text: DOI arXiv
Chang, Der-Chen; Kang, Qianqian; Wang, Wei The heat kernel of sub-Laplace operator on nilpotent Lie groups of step two. (English) Zbl 1455.35129 Appl. Anal. 100, No. 1, 17-36 (2021). MSC: 35K08 35R03 33C45 22E25 32W05 PDFBibTeX XMLCite \textit{D.-C. Chang} et al., Appl. Anal. 100, No. 1, 17--36 (2021; Zbl 1455.35129) Full Text: DOI
Mamon, S. V. The Wiener measure on the Heisenberg group and parabolic equations. (English. Russian original) Zbl 1478.60015 J. Math. Sci., New York 245, No. 2, 155-177 (2020); translation from Fundam. Prikl. Mat. 21, No. 4, 67-98 (2016). Reviewer: Vladimir V. Kisil (Leeds) MSC: 60B15 60J25 60J65 PDFBibTeX XMLCite \textit{S. V. Mamon}, J. Math. Sci., New York 245, No. 2, 155--177 (2020; Zbl 1478.60015); translation from Fundam. Prikl. Mat. 21, No. 4, 67--98 (2016) Full Text: DOI
Campbell, Joshua; Melcher, Tai Small-time asymptotics for subelliptic Hermite functions on \(SU(2)\) and the CR sphere. (English) Zbl 1472.58018 Potential Anal. 53, No. 3, 1063-1095 (2020). Reviewer: Viet-Anh Nguyen (Lille) MSC: 58J35 53C17 32V05 32V20 PDFBibTeX XMLCite \textit{J. Campbell} and \textit{T. Melcher}, Potential Anal. 53, No. 3, 1063--1095 (2020; Zbl 1472.58018) Full Text: DOI arXiv
Mamon, Sergeĭ Vladimirovich Solution of the Cauchy problem for the heat equation on the Heisenberg group and the Wiener integral. (English. Russian original) Zbl 1445.35189 Mosc. Univ. Math. Bull. 74, No. 6, 221-226 (2019); translation from Vestn. Mosk. Univ., Ser. I 74, No. 6, 8-14 (2019). MSC: 35K05 35R03 35K15 PDFBibTeX XMLCite \textit{S. V. Mamon}, Mosc. Univ. Math. Bull. 74, No. 6, 221--226 (2019; Zbl 1445.35189); translation from Vestn. Mosk. Univ., Ser. I 74, No. 6, 8--14 (2019) Full Text: DOI
Mamon, S. V. On the transfer of the Wiener measure to the set of continuous trajectories in the Heisenberg group. (English) Zbl 1452.28008 Russ. J. Math. Phys. 26, No. 4, 454-469 (2019). Reviewer: Daniel Beltiţă (Bucureşti) MSC: 28C20 22E25 58D20 PDFBibTeX XMLCite \textit{S. V. Mamon}, Russ. J. Math. Phys. 26, No. 4, 454--469 (2019; Zbl 1452.28008) Full Text: DOI
Mamon, S. V. On the Hölder property of trajectories in a set of full Wiener measure on the Heisenberg group. (English. Russian original) Zbl 1439.60045 Math. Notes 106, No. 2, 308-312 (2019); translation from Mat. Zametki 106, No. 2, 316-320 (2019). MSC: 60G51 60G57 47D06 PDFBibTeX XMLCite \textit{S. V. Mamon}, Math. Notes 106, No. 2, 308--312 (2019; Zbl 1439.60045); translation from Mat. Zametki 106, No. 2, 316--320 (2019) Full Text: DOI
Chang, Der-Chen; Chang, Shu-Cheng; Han, Yingbo; Tie, Jingzhi A CR analogue of Yau’s conjecture on pseudoharmonic functions of polynomial growth. (English) Zbl 1429.32050 Can. J. Math. 71, No. 6, 1367-1394 (2019). MSC: 32V05 32V20 53C56 PDFBibTeX XMLCite \textit{D.-C. Chang} et al., Can. J. Math. 71, No. 6, 1367--1394 (2019; Zbl 1429.32050) Full Text: DOI
Oka, Yasuyuki An existence and uniqueness result for the Navier-Stokes type equations on the Heisenberg group. (English) Zbl 1439.35504 J. Math. Anal. Appl. 473, No. 1, 382-407 (2019). MSC: 35R03 35A01 35A02 35Q30 PDFBibTeX XMLCite \textit{Y. Oka}, J. Math. Anal. Appl. 473, No. 1, 382--407 (2019; Zbl 1439.35504) Full Text: DOI
Wu, Qingyan; Fu, Zunwei Boundedness of Hausdorff operators on Hardy spaces in the Heisenberg group. (English) Zbl 06946296 Banach J. Math. Anal. 12, No. 4, 909-934 (2018). MSC: 47G10 22E25 26D15 42B30 PDFBibTeX XMLCite \textit{Q. Wu} and \textit{Z. Fu}, Banach J. Math. Anal. 12, No. 4, 909--934 (2018; Zbl 06946296) Full Text: DOI Euclid
Bruno, Tommaso; Calzi, Mattia Asymptotics for the heat kernel on H-type groups. (English) Zbl 1407.35094 Ann. Mat. Pura Appl. (4) 197, No. 4, 1017-1049 (2018). Reviewer: Andrei Perjan (Chişinău) MSC: 35K08 35R03 35P05 41A60 47A10 PDFBibTeX XMLCite \textit{T. Bruno} and \textit{M. Calzi}, Ann. Mat. Pura Appl. (4) 197, No. 4, 1017--1049 (2018; Zbl 1407.35094) Full Text: DOI arXiv
Wang, Haimeng; Wu, Qingyan On fundamental solution for powers of the sub-Laplacian on the Heisenberg group. (English) Zbl 1399.35006 Appl. Math., Ser. B (Engl. Ed.) 32, No. 3, 365-378 (2017). MSC: 35A08 35R03 PDFBibTeX XMLCite \textit{H. Wang} and \textit{Q. Wu}, Appl. Math., Ser. B (Engl. Ed.) 32, No. 3, 365--378 (2017; Zbl 1399.35006) Full Text: DOI
Wu, Qingyan; Fan, Dashan Hardy space estimates of Hausdorff operators on the Heisenberg group. (English) Zbl 1515.47058 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 164, 135-154 (2017). MSC: 47B90 42B30 22E25 26D15 PDFBibTeX XMLCite \textit{Q. Wu} and \textit{D. Fan}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 164, 135--154 (2017; Zbl 1515.47058) Full Text: DOI
Asaad, Malva; Gordina, Maria Hypoelliptic heat kernels on nilpotent Lie groups. (English) Zbl 1375.58020 Potential Anal. 45, No. 2, 355-386 (2016). Reviewer: Shu-Yu Hsu (Min-hsiung) MSC: 58J35 53C17 PDFBibTeX XMLCite \textit{M. Asaad} and \textit{M. Gordina}, Potential Anal. 45, No. 2, 355--386 (2016; Zbl 1375.58020) Full Text: DOI arXiv
Martini, Alessio; Müller, Detlef Spectral multipliers on 2-step groups: topological versus homogeneous dimension. (English) Zbl 1366.43002 Geom. Funct. Anal. 26, No. 2, 680-702 (2016). Reviewer: Öznur Kulak (Görele) MSC: 43A22 42B15 PDFBibTeX XMLCite \textit{A. Martini} and \textit{D. Müller}, Geom. Funct. Anal. 26, No. 2, 680--702 (2016; Zbl 1366.43002) Full Text: DOI arXiv
Bauer, Wolfram; Furutani, Kenro; Iwasaki, Chisato Fundamental solution of a higher step Grushin type operator. (English) Zbl 1310.35082 Adv. Math. 271, 188-234 (2015). MSC: 35H20 35A08 22E25 33C10 PDFBibTeX XMLCite \textit{W. Bauer} et al., Adv. Math. 271, 188--234 (2015; Zbl 1310.35082) Full Text: DOI
Petitot, Jean Landmarks for neurogeometry. (English) Zbl 1351.92009 Citti, Giovanna (ed.) et al., Neuromathematics of vision. Berlin: Springer (ISBN 978-3-642-34443-5/hbk; 978-3-642-34444-2/ebook). Lecture Notes in Morphogenesis, 1-85 (2014). MSC: 92C20 53Z05 53C17 92-02 PDFBibTeX XMLCite \textit{J. Petitot}, in: Neuromathematics of vision. Berlin: Springer. 1--85 (2014; Zbl 1351.92009) Full Text: DOI
Boscain, U.; Gauthier, J.-P.; Rossi, F. Hypoelliptic heat kernel over \(3\)-step nilpotent Lie groups. (English. Russian original) Zbl 1309.58001 J. Math. Sci., New York 199, No. 6, 614-628 (2014); translation from Sovrem. Mat., Fundam. Napravl. 42, 48-61 (2011). MSC: 58J35 22E25 53C17 42B37 22E30 43A80 PDFBibTeX XMLCite \textit{U. Boscain} et al., J. Math. Sci., New York 199, No. 6, 614--628 (2014; Zbl 1309.58001); translation from Sovrem. Mat., Fundam. Napravl. 42, 48--61 (2011) Full Text: DOI arXiv
Liu, Heping; Wang, Yingzhan Wiener measure for Heisenberg group. (English) Zbl 1303.28019 Sci. China, Math. 57, No. 8, 1605-1614 (2014). MSC: 28C20 60B15 60H05 PDFBibTeX XMLCite \textit{H. Liu} and \textit{Y. Wang}, Sci. China, Math. 57, No. 8, 1605--1614 (2014; Zbl 1303.28019) Full Text: DOI arXiv
Chang, Shu-Cheng; Fan, Yen-Wen; Tie, Jingzhi; Wu, Chin-Tung Matrix Li-Yau-Hamilton inequality for the CR heat equation in pseudohermitian \((2n+1)\)-manifolds. (English) Zbl 1310.53035 Math. Ann. 360, No. 1-2, 267-306 (2014). Reviewer: Vehbi Emrah Paksoy (Fort Lauderdale) MSC: 53C21 32V99 53C55 32Q99 PDFBibTeX XMLCite \textit{S.-C. Chang} et al., Math. Ann. 360, No. 1--2, 267--306 (2014; Zbl 1310.53035) Full Text: DOI
Calin, Ovidiu Transience of diffusions on Heisenberg and Grushin distributions. (English) Zbl 1282.93048 J. Geom. Phys. 77, 131-142 (2014). MSC: 93B05 49N99 PDFBibTeX XMLCite \textit{O. Calin}, J. Geom. Phys. 77, 131--142 (2014; Zbl 1282.93048) Full Text: DOI
Rossi, Francesco Large time behavior for the heat equation on Carnot groups. (English) Zbl 1268.35121 NoDEA, Nonlinear Differ. Equ. Appl. 20, No. 3, 1393-1407 (2013). MSC: 35R03 35H10 58J37 PDFBibTeX XMLCite \textit{F. Rossi}, NoDEA, Nonlinear Differ. Equ. Appl. 20, No. 3, 1393--1407 (2013; Zbl 1268.35121) Full Text: DOI arXiv
Duan, Xiaoxi The heat kernel and Green function of the sub-Laplacian on the Heisenberg group. (English) Zbl 1282.35392 Molahajloo, Shahla (ed.) et al., Pseudo-differential operators, generalized functions and asymptotics. Selected papers of the 8th ISAAC congress, Moscow, Russia, August 22–27, 2011. Basel: Birkhäuser/Springer (ISBN 978-3-0348-0584-1/hbk; 978-3-0348-0585-8/ebook). Operator Theory: Advances and Applications 231, 55-75 (2013). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 35R03 22E30 43A80 47F05 47G30 PDFBibTeX XMLCite \textit{X. Duan}, Oper. Theory: Adv. Appl. 231, 55--75 (2013; Zbl 1282.35392) Full Text: DOI
Diatta, B.; Ndomo, J. C.; Wafo Soh, C. An elementary symmetry-based derivation of the heat kernel on Heisenberg group. (English) Zbl 1337.35162 Afr. Diaspora J. Math. 14, No. 2, 82-89 (2012). MSC: 35R03 17B66 30H20 35A30 35K08 PDFBibTeX XMLCite \textit{B. Diatta} et al., Afr. Diaspora J. Math. 14, No. 2, 82--89 (2012; Zbl 1337.35162) Full Text: Euclid
Frank, Rupert L.; Lieb, Elliott H. Sharp constants in several inequalities on the Heisenberg group. (English) Zbl 1252.42023 Ann. Math. (2) 176, No. 1, 349-381 (2012). Reviewer: Giuseppe Di Fazio (Catania) MSC: 42B35 PDFBibTeX XMLCite \textit{R. L. Frank} and \textit{E. H. Lieb}, Ann. Math. (2) 176, No. 1, 349--381 (2012; Zbl 1252.42023) Full Text: DOI arXiv
Furutani, Kenro; Iwasaki, Chisato; Kagawa, Toshinao An action function for a higher step Grushin operator. (English) Zbl 1244.35062 J. Geom. Phys. 62, No. 9, 1949-1976 (2012). MSC: 35K05 22E25 PDFBibTeX XMLCite \textit{K. Furutani} et al., J. Geom. Phys. 62, No. 9, 1949--1976 (2012; Zbl 1244.35062) Full Text: DOI
Séguin, C.; Mansouri, A. Short-time asymptotics of heat kernels of hypoelliptic Laplacians on unimodular Lie groups. (English) Zbl 1253.43006 J. Funct. Anal. 262, No. 9, 3891-3928 (2012). Reviewer: Jean Ludwig (Metz) MSC: 43A80 22E30 58J35 PDFBibTeX XMLCite \textit{C. Séguin} and \textit{A. Mansouri}, J. Funct. Anal. 262, No. 9, 3891--3928 (2012; Zbl 1253.43006) Full Text: DOI
Bonnefont, Michel The subelliptic heat kernels on \(\mathbf{SL}(2,\mathbb{R})\) and on its universal covering \(\widetilde{\mathbf{SL}(2,\mathbb{R})}\): Integral representations and some functional inequalities. (English) Zbl 1236.43006 Potential Anal. 36, No. 2, 275-300 (2012). Reviewer: Dian K. Palagachev (Bari) MSC: 43A80 58J35 35H20 PDFBibTeX XMLCite \textit{M. Bonnefont}, Potential Anal. 36, No. 2, 275--300 (2012; Zbl 1236.43006) Full Text: DOI arXiv
Catană, Viorel The heat kernel and Green function of the generalized Hermite operator, and the abstract Cauchy problem for the abstract Hermite operator. (English) Zbl 1266.47068 Rodino, Luigi (ed.) et al., Pseudo-differential operators: analysis, applications and computations. Selected papers based on lectures presented at the meeting of the ISAAC Group in Pseudo-Differential Operators (IGPDO), London, UK, July 13–18, 2009. Basel: Birkhäuser (ISBN 978-3-0348-0048-8/hbk; 978-3-0348-0049-5/ebook). Operator Theory: Advances and Applications 213, 155-171 (2011). Reviewer: Matheus Cheque Bortolan (São Carlos) MSC: 47F05 47A75 47D06 35Q40 PDFBibTeX XMLCite \textit{V. Catană}, Oper. Theory: Adv. Appl. 213, 155--171 (2011; Zbl 1266.47068) Full Text: DOI
Boggess, Albert; Raich, Andrew The \(\square_b\)-heat equation on quadric manifolds. (English) Zbl 1222.32058 J. Geom. Anal. 21, No. 2, 256-275 (2011). Reviewer: Chiung-Jue Sung (Hsinchu) MSC: 32W30 33C45 35K08 58J35 PDFBibTeX XMLCite \textit{A. Boggess} and \textit{A. Raich}, J. Geom. Anal. 21, No. 2, 256--275 (2011; Zbl 1222.32058) Full Text: DOI arXiv
Catană, Viorel The heat equation for the generalized Hermite and the generalized Landau operators. (English) Zbl 1226.47043 Integral Equations Oper. Theory 66, No. 1, 41-52 (2010). Reviewer: Jin Liang (Shanghai) MSC: 47D06 47G10 47G30 35S10 PDFBibTeX XMLCite \textit{V. Catană}, Integral Equations Oper. Theory 66, No. 1, 41--52 (2010; Zbl 1226.47043) Full Text: DOI
Bauer, Wolfram; Furutani, Kenro Spectral zeta function of a sub-Laplacian on product sub-Riemannian manifolds and zeta-regularized determinant. (English) Zbl 1198.53032 J. Geom. Phys. 60, No. 9, 1209-1234 (2010). MSC: 53C17 58J50 PDFBibTeX XMLCite \textit{W. Bauer} and \textit{K. Furutani}, J. Geom. Phys. 60, No. 9, 1209--1234 (2010; Zbl 1198.53032) Full Text: DOI
Lust-Piquard, Françoise Ornstein-Uhlenbeck semi-groups on stratified groups. (English) Zbl 1192.47042 J. Funct. Anal. 258, No. 6, 1883-1908 (2010). Reviewer: Heinrich Hering (Rockenberg) MSC: 47D06 58J65 47D03 60J60 60B99 PDFBibTeX XMLCite \textit{F. Lust-Piquard}, J. Funct. Anal. 258, No. 6, 1883--1908 (2010; Zbl 1192.47042) Full Text: DOI arXiv
Calin, Ovidiu; Chang, Der-Chen; Fan, Haitao The heat kernel for Kolmogorov type operators and its applications. (English) Zbl 1184.35149 J. Fourier Anal. Appl. 15, No. 6, 816-838 (2009). MSC: 35K08 49L99 34K10 35H20 91B24 58J35 PDFBibTeX XMLCite \textit{O. Calin} et al., J. Fourier Anal. Appl. 15, No. 6, 816--838 (2009; Zbl 1184.35149) Full Text: DOI
Tie, Jingzhi; Wong, M. W. The heat kernel and Green functions of sub-Laplacians on the quaternion Heisenberg group. (English) Zbl 1176.35052 J. Geom. Anal. 19, No. 1, 191-210 (2009). MSC: 35H20 42B30 35R03 PDFBibTeX XMLCite \textit{J. Tie} and \textit{M. W. Wong}, J. Geom. Anal. 19, No. 1, 191--210 (2009; Zbl 1176.35052) Full Text: DOI
Baudoin, Fabrice; Bonnefont, Michel The subelliptic heat kernel on \(\mathbf{SU}(2)\): representations, asymptotics and gradient bounds. (English) Zbl 1189.58009 Math. Z. 263, No. 3, 647-672 (2009). Reviewer: Chun-Gil Park (Daejeon) MSC: 58J05 22E30 58J37 PDFBibTeX XMLCite \textit{F. Baudoin} and \textit{M. Bonnefont}, Math. Z. 263, No. 3, 647--672 (2009; Zbl 1189.58009) Full Text: DOI arXiv
Eldredge, Nathaniel Precise estimates for the subelliptic heat kernel on H-type groups. (English) Zbl 1178.35096 J. Math. Pures Appl. (9) 92, No. 1, 52-85 (2009). Reviewer: Marco Biroli (Milano) MSC: 35B45 35H20 53C17 PDFBibTeX XMLCite \textit{N. Eldredge}, J. Math. Pures Appl. (9) 92, No. 1, 52--85 (2009; Zbl 1178.35096) Full Text: DOI arXiv
Dragomir, Sorin; Lanconelli, Ermanno Subelliptic harmonic morphisms. (English) Zbl 1175.58005 Osaka J. Math. 46, No. 2, 411-440 (2009). Reviewer: Themistocles M. Rassias (Athens) MSC: 58E20 32V20 53C43 35H20 PDFBibTeX XMLCite \textit{S. Dragomir} and \textit{E. Lanconelli}, Osaka J. Math. 46, No. 2, 411--440 (2009; Zbl 1175.58005) Full Text: Euclid
Agrachev, Andrei; Boscain, Ugo; Gauthier, Jean-Paul; Rossi, Francesco The intrinsic hypoelliptic Laplacian and its heat kernel on unimodular Lie groups. (English) Zbl 1165.58012 J. Funct. Anal. 256, No. 8, 2621-2655 (2009). Reviewer: Dian K. Palagachev (Bari) MSC: 58J35 43A80 PDFBibTeX XMLCite \textit{A. Agrachev} et al., J. Funct. Anal. 256, No. 8, 2621--2655 (2009; Zbl 1165.58012) Full Text: DOI arXiv
Boggess, Albert; Raich, Andrew A simplified calculation for the fundamental solution to the heat equation on the Heisenberg group. (English) Zbl 1166.32023 Proc. Am. Math. Soc. 137, No. 3, 937-944 (2009). Reviewer: Vasile Oproiu (Iaşi) MSC: 32W30 33C45 42C10 PDFBibTeX XMLCite \textit{A. Boggess} and \textit{A. Raich}, Proc. Am. Math. Soc. 137, No. 3, 937--944 (2009; Zbl 1166.32023) Full Text: DOI arXiv
Yang, Qiaohua; Zhu, Fuliu The heat kernel on H-type groups. (English) Zbl 1134.22006 Proc. Am. Math. Soc. 136, No. 4, 1457-1464 (2008). Reviewer: Gheorghe Zet (Iaşi) MSC: 22E25 35A08 PDFBibTeX XMLCite \textit{Q. Yang} and \textit{F. Zhu}, Proc. Am. Math. Soc. 136, No. 4, 1457--1464 (2008; Zbl 1134.22006) Full Text: DOI
Dasgupta, Aparajita; Wong, M. W. Weyl transforms and the heat equation for the sub-Laplacian on the Heisenberg group. (English) Zbl 1173.47029 Rodino, Luigi (ed.) et al., New developments in pseudo-differential operators. Selected papers of the 6th congress of the International Society for Analysis, its Applications and Computation (ISAAC), the ISAAC Group in Pseudo-Differential Operators (IGPDO), Middle East Technical University, Ankara, Turkey, August 13–18, 2007. Basel: Birkhäuser (ISBN 978-3-7643-8968-0/hbk). Operator Theory: Advances and Applications 189, 33-42 (2009). Reviewer: Anatoly N. Kochubei (Kyïv) MSC: 47F05 35H20 47G30 58J35 PDFBibTeX XMLCite \textit{A. Dasgupta} and \textit{M. W. Wong}, Oper. Theory: Adv. Appl. 189, 33--42 (2007; Zbl 1173.47029) Full Text: DOI
Feinsilver, Ph.; Pap, G. Calculation of Fourier transforms of a Brownian motion on the Heisenberg group using splitting formulas. (English) Zbl 1166.60003 J. Funct. Anal. 249, No. 1, 1-30 (2007). MSC: 60B15 60J65 47D07 43A05 43A30 PDFBibTeX XMLCite \textit{Ph. Feinsilver} and \textit{G. Pap}, J. Funct. Anal. 249, No. 1, 1--30 (2007; Zbl 1166.60003) Full Text: DOI
Li, Hong-Quan Asymptotic estimates for the heat kernel on Heisenberg groups. (Estimations asymptotiques du noyau de la chaleur sur les groupes de Heisenberg.) (French. Abridged English version) Zbl 1114.22007 C. R., Math., Acad. Sci. Paris 344, No. 8, 497-502 (2007). MSC: 35R03 58J35 35K05 22E30 43A80 PDFBibTeX XMLCite \textit{H.-Q. Li}, C. R., Math., Acad. Sci. Paris 344, No. 8, 497--502 (2007; Zbl 1114.22007) Full Text: DOI
Li, Hong-Quan Estimation optimale du gradient du semi-groupe de la chaleur sur le groupe de Heisenberg. (Optimal estimation of the gradient of the heat semigroup on the Heisenberg group.) (French) Zbl 1106.22009 J. Funct. Anal. 236, No. 2, 369-394 (2006). Reviewer: Jean Ludwig (Metz) MSC: 35R03 35K05 58J35 22E30 PDFBibTeX XMLCite \textit{H.-Q. Li}, J. Funct. Anal. 236, No. 2, 369--394 (2006; Zbl 1106.22009) Full Text: DOI
Luan, Jing Wen; Zhu, Fu Liu Asymptotics for certain harmonic functions and the Martin compactification on the quaternionic Heisenberg group. (English) Zbl 1101.22007 Acta Math. Sin., Engl. Ser. 21, No. 6, 1295-1308 (2005). Reviewer: Lubomira Softova (Bari) MSC: 22E30 22E25 31C35 PDFBibTeX XMLCite \textit{J. W. Luan} and \textit{F. L. Zhu}, Acta Math. Sin., Engl. Ser. 21, No. 6, 1295--1308 (2005; Zbl 1101.22007) Full Text: DOI
Applebaum, David; Cohen, Serge Lévy processes, pseudo-differential operators and Dirichlet forms in the Heisenberg group. (English) Zbl 1075.60048 Ann. Fac. Sci. Toulouse, VI. Sér., Math. 13, No. 2, 149-177 (2004). Reviewer: Kun Soo Chang (Seoul) MSC: 60G51 58J65 35S05 31C25 60J25 47G30 PDFBibTeX XMLCite \textit{D. Applebaum} and \textit{S. Cohen}, Ann. Fac. Sci. Toulouse, Math. (6) 13, No. 2, 149--177 (2004; Zbl 1075.60048) Full Text: DOI Numdam EuDML Link
Beals, Richard; Gaveau, Bernard; Greiner, Peter; Kannai, Yakar Transversally elliptic operators. (English) Zbl 1125.35302 Bull. Sci. Math. 128, No. 7, 531-576 (2004). MSC: 35A08 35H20 35J70 35K65 PDFBibTeX XMLCite \textit{R. Beals} et al., Bull. Sci. Math. 128, No. 7, 531--576 (2004; Zbl 1125.35302) Full Text: DOI
Narayanan, E. K.; Thangavelu, S. Injectivity sets for spherical means on the Heisenberg group. (English) Zbl 0995.43003 J. Math. Anal. Appl. 263, No. 2, 565-579 (2001). Reviewer: K.Saka (Akita) MSC: 43A80 22E30 PDFBibTeX XMLCite \textit{E. K. Narayanan} and \textit{S. Thangavelu}, J. Math. Anal. Appl. 263, No. 2, 565--579 (2001; Zbl 0995.43003) Full Text: DOI
Chang, Der-Chen; Tie, Jingzhi Estimates for powers of sub-Laplacian on the non-isotropic Heisenberg group. (English) Zbl 0985.22004 J. Geom. Anal. 10, No. 4, 653-678 (2000). Reviewer: Jan Chrastina (Brno) MSC: 22E30 35A08 PDFBibTeX XMLCite \textit{D.-C. Chang} and \textit{J. Tie}, J. Geom. Anal. 10, No. 4, 653--678 (2000; Zbl 0985.22004) Full Text: DOI
Chang, Der-Chen; Tie, Jingzhi Estimates for powers of sub-Laplacian on the non-isotropic Heisenberg group. (English) Zbl 0992.22007 J. Geom. Anal. 10, No. 4, 653-678 (2000). Reviewer: Der-Chen Chang (College Park) MSC: 22E27 58J05 PDFBibTeX XML Full Text: DOI
Coulhon, Thierry; Müller, Detlef; Zienkiewicz, Jacek About Riesz transforms on the Heisenberg groups. (English) Zbl 0859.22006 Math. Ann. 305, No. 2, 369-379 (1996). Reviewer: A.F.M.ter Elst (Eindhoven) MSC: 22E30 43A80 42B20 58J35 PDFBibTeX XMLCite \textit{T. Coulhon} et al., Math. Ann. 305, No. 2, 369--379 (1996; Zbl 0859.22006) Full Text: DOI EuDML
Beals, Richard; Gaveau, Bernard; Greiner, Peter On a geometric formula for the fundamental solution of subelliptic Laplacians. (English) Zbl 0864.35005 Math. Nachr. 181, 81-163 (1996). Reviewer: H.Tanabe (Toyonaka) MSC: 35A08 35J70 35N15 PDFBibTeX XMLCite \textit{R. Beals} et al., Math. Nachr. 181, 81--163 (1996; Zbl 0864.35005) Full Text: DOI
Randall, Jennifer The heat kernel for generalized Heisenberg groups. (English) Zbl 0897.43007 J. Geom. Anal. 6, No. 2, 287-316 (1996). Reviewer: J.Randall (Kensington/NSW) MSC: 43A80 35A08 58J35 PDFBibTeX XMLCite \textit{J. Randall}, J. Geom. Anal. 6, No. 2, 287--316 (1996; Zbl 0897.43007) Full Text: DOI
Jørgensen, Palle E. T. Extensions of positive definite integral kernels on the Heisenberg group. (English) Zbl 0709.46021 J. Funct. Anal. 92, No. 2, 474-508 (1990). Reviewer: I.Ciorănescu MSC: 46F25 PDFBibTeX XMLCite \textit{P. E. T. Jørgensen}, J. Funct. Anal. 92, No. 2, 474--508 (1990; Zbl 0709.46021) Full Text: DOI
Jørgensen, Palle E. T. Second-order right-invariant partial differential equations on a Lie group. (English) Zbl 0703.35131 J. Math. Anal. Appl. 142, No. 2, 337-354 (1989). Reviewer: F.M.Ragab MSC: 35P10 35J05 43A80 PDFBibTeX XMLCite \textit{P. E. T. Jørgensen}, J. Math. Anal. Appl. 142, No. 2, 337--354 (1989; Zbl 0703.35131) Full Text: DOI
Jørgensen, Palle E. T. Positive definite functions on the Heisenberg group. (English) Zbl 0702.43004 Math. Z. 201, No. 4, 455-476 (1989). Reviewer: J.Lacroix MSC: 43A35 22E27 PDFBibTeX XMLCite \textit{P. E. T. Jørgensen}, Math. Z. 201, No. 4, 455--476 (1989; Zbl 0702.43004) Full Text: DOI EuDML
Hueber, H.; Müller, D. Asymptotics for some Green kernels on the Heisenberg group and the Martin boundary. (English) Zbl 0639.31005 Math. Ann. 283, No. 1, 97-119 (1989). Reviewer: H.Hueber MSC: 31C05 31C35 35A08 35K05 PDFBibTeX XMLCite \textit{H. Hueber} and \textit{D. Müller}, Math. Ann. 283, No. 1, 97--119 (1989; Zbl 0639.31005) Full Text: DOI EuDML
Bratteli, Ola; Goodman, Frederick M.; Jørgensen, Palle E. T.; Robinson, Derek W. The heat semigroup and integrability of Lie algebras. (English) Zbl 0662.22009 J. Funct. Anal. 79, No. 2, 351-397 (1988). Reviewer: Joachim Hilgert (Paderborn) MSC: 22E45 47D03 17B15 PDFBibTeX XMLCite \textit{O. Bratteli} et al., J. Funct. Anal. 79, No. 2, 351--397 (1988; Zbl 0662.22009) Full Text: DOI
Jørgensen, Palle E. T.; Klink, William H. Spectral transform for the sub-Laplacian on the Heisenberg group. (English) Zbl 0656.43006 J. Anal. Math. 50, 101-121 (1988). Reviewer: M.Monastyrsky MSC: 43A80 37J99 35K05 22E70 81T60 22E25 22E27 PDFBibTeX XMLCite \textit{P. E. T. Jørgensen} and \textit{W. H. Klink}, J. Anal. Math. 50, 101--121 (1988; Zbl 0656.43006) Full Text: DOI
Helmes, K.; Schwane, A. Levy’s stochastic area formula in higher dimensions. (English) Zbl 0522.60082 J. Funct. Anal. 54, 177-192 (1983). MSC: 60J60 60J25 60J65 58J65 65H10 60H15 PDFBibTeX XMLCite \textit{K. Helmes} and \textit{A. Schwane}, J. Funct. Anal. 54, 177--192 (1983; Zbl 0522.60082) Full Text: DOI
Stanton, Nancy K. The heat equation for the d-Neumann problem in a strictly pseudoconvex Siegel domain. (English) Zbl 0469.35071 J. Anal. Math. 38, 67-112 (1980). MSC: 35N15 32W05 58J35 32T99 PDFBibTeX XMLCite \textit{N. K. Stanton}, J. Anal. Math. 38, 67--112 (1980; Zbl 0469.35071) Full Text: DOI
Gaveau, Bernard Least action principle, heat propagation and subelliptic estimates on certain nilpotent groups. (Principe de moindre action, propagation de la chaleur et estimées sous elliptiques sur certains groupes nilpotents.) (French) Zbl 0366.22010 Acta Math. 139, 95-153 (1977). MSC: 22E30 35H20 58J05 58J35 58J65 60J60 22E25 PDFBibTeX XMLCite \textit{B. Gaveau}, Acta Math. 139, 95--153 (1977; Zbl 0366.22010) Full Text: DOI