Spectral asymptotics for multi-quasi-elliptic operators in ℝ n

P. Boggiatto; E. Buzano

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (1997)

  • Volume: 24, Issue: 3, page 511-536
  • ISSN: 0391-173X

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Boggiatto, P., and Buzano, E.. "Spectral asymptotics for multi-quasi-elliptic operators in $\mathbb {R}^n$." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 24.3 (1997): 511-536. <http://eudml.org/doc/84268>.

@article{Boggiatto1997,
author = {Boggiatto, P., Buzano, E.},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {eigenvalues counting function; asymptotic expansion; Weyl term},
language = {eng},
number = {3},
pages = {511-536},
publisher = {Scuola normale superiore},
title = {Spectral asymptotics for multi-quasi-elliptic operators in $\mathbb \{R\}^n$},
url = {http://eudml.org/doc/84268},
volume = {24},
year = {1997},
}

TY - JOUR
AU - Boggiatto, P.
AU - Buzano, E.
TI - Spectral asymptotics for multi-quasi-elliptic operators in $\mathbb {R}^n$
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 1997
PB - Scuola normale superiore
VL - 24
IS - 3
SP - 511
EP - 536
LA - eng
KW - eigenvalues counting function; asymptotic expansion; Weyl term
UR - http://eudml.org/doc/84268
ER -

References

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  1. [1] P. Boggiatto - E. Buzano - L. Rodino, Multi-quasi-elliptic operators in R n, In: Demuth M. - Schulze B.-W. (eds) "Operator Theory: Advances and Applications" Birkhäuser Verlag, Base, Switzerland 1995. Zbl0884.35186MR1365315
  2. [2] P. Boggiatto, Spazi di Sobolev associati ad un poliedro ed operatori pseudodifferenziali multi-quasi-ellittici in Rn, Boll. Un. Mat. Ital.B7 (1993), 511-548. Zbl0807.35168MR1244406
  3. [3] P. Boggiatto, Sobolev spaces associated to a polyhedron and Fourier integral operators in Rn, Ann. Mat. Pura Appl. (IV), 171 (1996), 15-40. Zbl0881.35134MR1441863
  4. [4] L. Cattabriga, Su una classe di polinomi ipoelittici, Rend. Sem. Mat. Univ. Padova36 (1966), 60-74. Zbl0144.06601MR206500
  5. [5] L. Cattabriga, Alcuni teoremi di immersione per spazifunzionali generalizzanti gli spazi di S. L. Sobolev, Ann. Univ. Ferrara12 (1967), 63-88. Zbl0165.47203MR229021
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  7. [7] J. Friberg, Multi-quasi-elliptic polynomials, Ann. Scuola Norm. Sup. Pisa Cl. Sci.21 (1967), 239-260. Zbl0161.07803MR221090
  8. [8] J. Friberg, Asymptotic behavior ofintergrals connected with spectral functions for hypoelliptic operators, Ark. Mat.7 (1967), 283-298. Zbl0154.35503MR221091
  9. [9] B. Helffer - D. Robert, Propriétés asymptotiques du spectre d'opérateurs pseudo-différentiels sur Rn, Comm. Partial Differential Equations7 (1982), 795-882. Zbl0501.35081MR662451
  10. [10] B. Helffer - D. Robert, Comportement semi-classique du spectre des hamiltoniens quantiques hypoelliptiques, Ann. Scuola Norm. Sup. Pisa Cl. Sci. 9 (1982), 405-431. Zbl0507.35066MR681933
  11. [11] V.P. Miha, The Behavior at infinity of a class of polynomials, Proc. Steklov Inst. Math.91 (1967), 65-86. Zbl0186.42602MR220886
  12. [12] A. Mohamed, Comportement asymptotique, avec estimation du reste, des valeurs propres d'une classe d'opérateurs pseudo-différentiels sur Rn, Math. Nachr. 140 (1989), 127-186. [13] B. Pini, Osservazioni sulla ipoellitticità, Boll. Un. Mat. Ital.B18 (1963), 420-432. Zbl0689.35067MR1015393
  13. [14] M.A. Shubin, Pseudodifferential Operators and Spectral Theory, Springer-Verlag, Berlin, 1987. Zbl0616.47040MR883081
  14. [15] V.N. Tulovski - M.A. Shubin, On asymptotic distribution of eigenvalues of pseudodifferential operators in Rn, Math USSR-Sb. 21 (1973), 565-583. Zbl0295.35068
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  16. [17] L. Zanghirati, Iterati di una classe di operatori ipoellittici e classi generalizzate di Gevrey, Analisi Funz. Appl. Supp. Boll. Un. Mat. Ital. 1 (1980), 177-195. Zbl0447.35023

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