The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms

Wiesław Cupała

Studia Mathematica (1995)

  • Volume: 113, Issue: 2, page 109-125
  • ISSN: 0039-3223

Abstract

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The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.

How to cite

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Cupała, Wiesław. "The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms." Studia Mathematica 113.2 (1995): 109-125. <http://eudml.org/doc/216164>.

@article{Cupała1995,
abstract = {The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.},
author = {Cupała, Wiesław},
journal = {Studia Mathematica},
keywords = {eigenvalue asymptotics; Dirichlet form; Markov process; Lie group; Hunt process; Markov processes; Lie groups; eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials; Markovian semigroup},
language = {eng},
number = {2},
pages = {109-125},
title = {The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms},
url = {http://eudml.org/doc/216164},
volume = {113},
year = {1995},
}

TY - JOUR
AU - Cupała, Wiesław
TI - The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms
JO - Studia Mathematica
PY - 1995
VL - 113
IS - 2
SP - 109
EP - 125
AB - The theory of Markov processes and the analysis on Lie groups are used to study the eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials.
LA - eng
KW - eigenvalue asymptotics; Dirichlet form; Markov process; Lie group; Hunt process; Markov processes; Lie groups; eigenvalue asymptotics of Dirichlet forms perturbed by scalar potentials; Markovian semigroup
UR - http://eudml.org/doc/216164
ER -

References

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  1. [1] K. L. Chung, Lectures from Markov Processes to Brownian Motion, Springer, 1982. Zbl0503.60073
  2. [2] W. Cupała, On the essential spectrum and eigenvalue asymptotics of certain Schrödinger operators, Studia Math. 96 (1990), 196-202. Zbl0716.35058
  3. [3] W. Cupała, On the eigenvalue asymptotics of certain Schrödinger operators, ibid. 105 (1993), 101-104. Zbl0811.35024
  4. [4] M. Cwikel, Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. of Math. 106 (1977), 93-100. Zbl0362.47006
  5. [5] C. L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206. Zbl0526.35080
  6. [6] C. L. Fefferman and D. H. Phong, On the asymptotic eigenvalue distribution of a pseudo-differential operator, Proc. Nat. Acad. Sci. U.S.A. 77 (1980), 5622-5625. Zbl0443.35082
  7. [7] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207. Zbl0312.35026
  8. [8] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, 1980. Zbl0422.31007
  9. [9] Y. Guivarc'h, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973), 333-379. Zbl0294.43003
  10. [10] L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 192-218. Zbl0164.13201
  11. [11] E. Lieb, The number of bound states of one-body Schrödinger operators and the Weyl problem, unpublished. Zbl0445.58029
  12. [12] K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216. Zbl0008.11301
  13. [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, 1979. Zbl0405.47007
  14. [14] G. V. Rosenblum, The distribution of the dicrete spectrum of singular differential operators, Dokl. Akad. Nauk SSSR 202 (1972), 1012-1015 (in Russian). 
  15. [15] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1977), 247-320. Zbl0346.35030
  16. [16] N. T. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260. Zbl0608.47047
  17. [17] N. T. Varopoulos, Analysis on Lie groups, ibid. 76 (1988), 346-410. Zbl0634.22008

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