Weyl formula for hypoelliptic operators of Schrödinger type
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- by Ernesto Buzano and Andrea Ziggioto PDF
- Proc. Amer. Math. Soc. 131 (2003), 265-274 Request permission
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
- Paolo Boggiatto, Ernesto Buzano, and Luigi Rodino, Global hypoellipticity and spectral theory, Mathematical Research, vol. 92, Akademie Verlag, Berlin, 1996. MR 1435282
- Ernesto Buzano, Some remarks on the Weyl asymptotics by the approximate spectral projection method, Boll. Unione Mat. Ital. Sez. B Artic. Ric. Mat. (8) 3 (2000), no. 3, 775–792 (English, with Italian summary). MR 1801620
- Ernesto Buzano and Andrea Ziggioto, Weyl formula for multi-quasi-elliptic operators of Schrödinger type, Ann. Mat. Pura Appl. (4) 180 (2001), no. 2, 223–243. MR 1847406, DOI 10.1007/s10231-001-8204-3
- Buzano, E. and Nicola, F., Hypoelliptic symbols and complex powers of pseudodifferential operators in the Weyl-Hörmander classes, in preparation.
- Nils Dencker, The Weyl calculus with locally temperate metrics and weights, Ark. Mat. 24 (1986), no. 1, 59–79. MR 852826, DOI 10.1007/BF02384389
- L. Hörmander, The Weyl calculus of pseudodifferential operators, Comm. Pure Appl. Math. 32 (1979), no. 3, 360–444. MR 517939, DOI 10.1002/cpa.3160320304
- Lars Hörmander, On the asymptotic distribution of the eigenvalues of pseudodifferential operators in $\textbf {R}^{n}$, Ark. Mat. 17 (1979), no. 2, 297–313. MR 608322, DOI 10.1007/BF02385475
- Lars Hörmander, The analysis of linear partial differential operators. I, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 256, Springer-Verlag, Berlin, 1983. Distribution theory and Fourier analysis. MR 717035, DOI 10.1007/978-3-642-96750-4
- Nils Nilsson, Monodromy and asymptotic properties of certain multiple integrals, Ark. Mat. 18 (1980), no. 2, 181–198. MR 608335, DOI 10.1007/BF02384689
- M. A. Shubin, Pseudodifferential operators and spectral theory, Springer Series in Soviet Mathematics, Springer-Verlag, Berlin, 1987. Translated from the Russian by Stig I. Andersson. MR 883081, DOI 10.1007/978-3-642-96854-9
- Michael E. Taylor, Pseudodifferential operators, Princeton Mathematical Series, No. 34, Princeton University Press, Princeton, N.J., 1981. MR 618463
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
- Received by editor(s): September 4, 2001
- Published electronically: June 12, 2002
- Communicated by: David S. Tartakoff
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 265-274
- MSC (2000): Primary 35P20, 47B06
- DOI: https://doi.org/10.1090/S0002-9939-02-06701-1
- MathSciNet review: 1929046