In this paper, we give an explicit formula for the Szegő kernel for (0, q) forms on the Heisenberg group Hn+1.
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Boutet de Monvel, L., Sjöstrand, J.: Sur la singularité des noyaux de Bergman et de Szegö. Astérisque, 34–35, 123–164 (1976)
Cheng, J. H., Malchiodi, A., Yang, P.: A positive mass theorem in three dimensional Cauchy–Riemann geometry. Adv. Math., 308, 276–347 (2017)
Chen, S. C., Shaw, M. C.: Partial Differential Equations in Several Complex Variables, AMS/IP Studies in Advanced Mathematics, 19, American Mathematical Society, Providence, RI; International Press, Boston, MA, 2001
Grigis, A., Sjöstrand, J.: Microlocal Analysis for Differential Operators, London Mathematical Society Lecture Note Series, vol. 196, Cambridge University Press, Cambridge, 1994
Hsiao, C. Y.: Projections in several complex variables. Mém. Soc. Math. France, Nouv. Sér., 123, 131 (2010)
Hsiao, C. Y., Marinescu, G.: On the singularities of the Szegő projections on lower energy forms. J. Differential Geom., 107(1), 83–155 (2017)
Hsiao, C. Y., Marinescu, G.: Szegő kernel asymptotics and morse inequalties on CR manifolds. Math. Z., 271, 509–553 (2012)
Hsiao, C. Y., Yung, P. Y.: The tangential Cauchy–Riemann complex on the heisenberg group via conformal invariance. Bull. Inst. Math. Acad. Sin. (N.S.), 8(3), 359–375 (2013)
Hsiao, C. Y., Yung, P. Y.: Solving the Kohn Laplacian on asymptotically flat CR manifolds of dimension 3. Adv. Math., 281, 734–822 (2015)
Hua, L. K.: Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Transl. of Math. Monographs 6, American Math. Society, 1963
Ma, X., Marinescu, G.: Holomorphic Morse Inequalities and Bergman Kernels. Progress in Math., 254, Birkhäuser Verlag, Basel, 2007
Szegő, G.: über orthogonalsysteme von polynomen. Math. Z., 4, 139–151 (1919)
The authors would like to thank the Institute for Mathematics, National University of Singapore for hospitality, a comfortable accommodation and financial support during their visits in May, 2017 for the program “Complex Geometry, Dynamical Systems and Foliation Theory”. A main part of this work was done when the first and third author were visiting the Institute of Mathematics, Academia Sinica in January, 2017. The authors thank the referees for carefully reading the manuscript and giving useful advices which improve the presentation of this paper.
In Memory of Professor Qikeng Lu (1927–2015)
The first author was partially supported by the CRC TRR 191: “Symplectic Structures in Geometry, Algebra and Dynamics”; the second author was partially supported by Taiwan Ministry of Science of Technology project (Grant No. 104-2628-M-001-003-MY2) and the Golden-Jade fellowship of Kenda Foundation; the third author was supported by National Natural Science Foundation of China (Grant No. 11501422)
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Herrmann, H., Hsiao, C.Y. & Li, X.S. An Explicit Formula for Szegő Kernels on the Heisenberg Group. Acta. Math. Sin.-English Ser. 34, 1225–1247 (2018). https://doi.org/10.1007/s10114-018-7324-2
- Heisenberg group
- Szegő kernels
- complex Fourier integral operators
MR(2010) Subject Classification