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On the positivstellensatz in Weyl's algebra
Author(s):
Joules
Nahas
Journal:
Proc. Amer. Math. Soc.
138
(2010),
987-995.
MSC (2010):
Primary 47L80
Posted:
October 21, 2009
MathSciNet review:
2566565
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Abstract:
We use harmonic analysis tools on the Heisenberg group to prove decay and regularity properties for a certain class of partial differential equations. These properties allow us to relax a technical condition for a sum of squares decomposition for the Weyl algebra.
References:
-
- 1.
- R. Bochnak, M. Coste, M-F. Roy,
Géométrie algébrique réelle,
Springer-Verlag, Berlin, 1980. - 2.
- L.C. Evans,
Partial Differential Equations,
American Mathematical Society, Providence, RI, 2000. MR 1625845 (99e:35001) - 3.
- G. B. Folland,
Harmonic Analysis in Phase Space,
Princeton University Press, Princeton, NJ, 1989. MR 983366 (92k:22017) - 4.
- R. Howe,
Quantum Mechanics and Partial Differential Equations,
J. Funct. Anal. 38 (1980), 188-254. MR 587908 (83b:35166) - 5.
- T. Kato,
On the Commutation Relation AB-BA=c,
Arch. Rat. Mech. Anal. 10 (1962), 273-275. MR 0151867 (27:1850) - 6.
- M. Putinar, J. W. Helton,
Positive Polynomials in Scalar and Matrix Variables, the Spectral Theorem, and Optimization,
in Operator Theory, Structured Matrices, and Dilations, Theta, Bucharest, June 1988, pp. 229-306. MR 2389626 - 7.
- R. Richtmeyer,
Principles of Advanced Mathematical Physics, Vol. 1,
Springer, New York, 1978. - 8.
- K. Schmüdgen,
A Strict Positivstellensatz for the Weyl Algebra,
Math. Ann. 331 (2005), 779-794. MR 2148796 (2007h:47127) - 9.
- K. Schmüdgen,
A Strict Positivstellensatz for Enveloping Algebras,
Math. Z. 254 (2006), 641-653. MR 2244371 (2007m:22007)
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Additional Information:
Joules
Nahas
Affiliation:
Department of Mathematics, University of California Santa Barbara, South Hall 6607, Santa Barbara, California 93106
Email:
nahas@math.uesb.edu
DOI:
10.1090/S0002-9939-09-10114-4
PII:
S 0002-9939(09)10114-4
Received by editor(s):
October 10, 2008,
Received by editor(s) in revised form:
November 9, 2008, and July 8, 2009
Posted:
October 21, 2009
Communicated by:
Nigel J. Kalton
Copyright of article:
Copyright
2009,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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