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Proceedings of the American Mathematical Society
ISSN 1088-6826 (e) ISSN 0002-9939 (p)
     

Weyl formula for hypoelliptic operators of Schrödinger type

Author(s): Ernesto Buzano; Andrea Ziggioto
Journal: Proc. Amer. Math. Soc. 131 (2003), 265-274.
MSC (2000): Primary 35P20, 47B06
Posted: June 12, 2002
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Abstract: In this work we consider a general class of hypoelliptic operators, for which we give an estimate of the remainder of the so-called Weyl asymptotic formula for the eigenvalues.


References:

1.
Boggiatto, P., Buzano, E. and Rodino, L., Global hypoellipticity and spectral theory, Mathematical Research, vol. 92, Akademie Verlag, Berlin, 1996.MR 97m:35040

2.
Buzano, E., Some remarks on the Weyl asymptotics by the approximate spectral projection method, Boll. U.M.I. 3-B (2000), no. 8, 775-792MR 2001k:35232

3.
Buzano, E. and Ziggioto, A., Weyl formula for multi-quasi-elliptic operators of Schrödinger type, Ann. Mat. Pura Appl. 180 (2001), 223-243.MR 2002f:35179

4.
Buzano, E. and Nicola, F., Hypoelliptic symbols and complex powers of pseudodifferential operators in the Weyl-Hörmander classes, in preparation.

5.
Dencker, N., The Weyl calculus with locally temperate metrics and weights, Arkiv för Mat. 24 (1986), 59-79.MR 87m:47111

6.
Hörmander, L., The Weyl calculus of pseudo-differential operators, Comm. Pure Appl. Math. 32 (1979), 359-443.MR 80j:47060

7.
-, On the asymptotic distribution of the eigenvalues of pseudodifferential operators in $\mathbb{R} ^n$, Arkiv för Mat. 17 (1979), 297-313.MR 82i:35140

8.
-, The analysis of linear partial differential operators II, Grundleheren der mathematischen Wissenschaften, vol. 257, Springer-Verlag, Berlin, 1983.MR 85g:35002b

9.
Nilsson, N., Monodromy and asymptotic properties of certain multiple integrals, Arkiv för Mat. 18 (1980), 181-198. MR 83i:32020

10.
Shubin, M. A., Pseudodifferential operators and spectral theory, Springer-Verlag, Berlin, 1987. MR 88c:47105

11.
Taylor M. E., Pseudodifferential Operators, Princeton Mathematical Series, vol. 34, Princeton University Press, Princeton, New Jersey, 1981. MR 82i:35172

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Additional Information:

Ernesto Buzano
Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italia
Email: buzano@dm.unito.it

Andrea Ziggioto
Affiliation: Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123 Torino, Italia
Email: ziggioto@dm.unito.it

DOI: 10.1090/S0002-9939-02-06701-1
PII: S 0002-9939(02)06701-1
Received by editor(s): September 4, 2001
Posted: June 12, 2002
Communicated by: David S. Tartakoff
Copyright of article: Copyright 2002, American Mathematical Society


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