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Spectrum of the  -Neumann Laplacian on polydiscs
Author(s):
Siqi
Fu
Journal:
Proc. Amer. Math. Soc.
135
(2007),
725-730.
MSC (2000):
Primary 32W05
Posted:
August 10, 2006
MathSciNet review:
2262868
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References |
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Abstract:
The spectrum of the  -Neumann Laplacian on a polydisc in  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:
-
- [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
 with the  -Neumann Laplacian, preprint, arXiv:math.CV/0508475. - [FS01]
- Siqi Fu and Emil J. Straube, Compactness in the
 -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
 -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
Email:
sfu@camden.rutgers.edu
DOI:
10.1090/S0002-9939-06-08656-4
PII:
S 0002-9939(06)08656-4
Received by editor(s):
September 20, 2005
Posted:
August 10, 2006
Additional Notes:
This research was supported in part by an NSF grant.
Communicated by:
Mei-Chi Shaw
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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