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Spectrum of the $ \overline{\partial}$-Neumann Laplacian on polydiscs

Author: Siqi Fu
Journal: Proc. Amer. Math. Soc. 135 (2007), 725-730
MSC (2000): Primary 32W05
Published electronically: August 10, 2006
MathSciNet review: 2262868
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Abstract: The spectrum of the $ \overline{\partial}$-Neumann Laplacian on a polydisc in $ \mathbb{C}^n$ is explicitly computed. The calculation exhibits that the spectrum consists of eigenvalues, some of which, in particular the smallest ones, are of infinite multiplicity.

References [Enhancements On Off] (What's this?)

  • [CS99] So-Chin Chen and Mei-Chi Shaw, Partial differential equations in several complex variables, AMS/IP, 2000. MR 1800297 (2001m:32071)
  • [Dav95] E. B. Davies, Spectral theory and differential operators, Cambridge University Press, 1995. MR 1349825 (96h:47056)
  • [Fo72] G. B. Folland, The tangential Cauchy-Riemann complex on spheres, Trans. Amer. Math. Soc. 171 (1972), 83-133. MR 0309156 (46:8266)
  • [FoK72] G. B. Folland and J. J. Kohn, The Neumann problem for the Cauchy-Riemann complex, Annals of Mathematics Studies, no. 75, Princeton University Press, 1972. MR 0461588 (57:1573)
  • [Fu05a] Siqi Fu, Hearing pseudoconvexity with the Kohn Laplacian, Mathematische Annalen 331 (2005), 475-485. MR 2115465 (2005i:32044)
  • [Fu05b] -, Hearing the type of a domain in $ \mathbb{C}^2$ with the $ \overline\partial$-Neumann Laplacian, preprint, arXiv:math.CV/0508475.
  • [FS01] Siqi Fu and Emil J. Straube, Compactness in the $ \overline\partial$-Neumann problem, Complex Analysis and Geometry, Proceedings of Ohio State University Conference, Walter De Gruyter, 9 (2001), 141-160. MR 1912737 (2004d:32053)
  • [K88] Steven G. Krantz, Compactness of the $ \overline\partial$-Neumann operator, Proc. Amer. Math. Soc. 103 (1988), no. 4, 1136-1138. MR 0954995 (89f:32032)
  • [W48] G. N. Watson, A treatise on Bessel Functions, 2nd edition, Cambridge, 1948.

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Additional Information

Siqi Fu
Affiliation: Department of Mathematical Sciences, Rutgers University-Camden, Camden, New Jersey 08102

Received by editor(s): September 20, 2005
Published electronically: August 10, 2006
Additional Notes: This research was supported in part by an NSF grant.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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