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.
@article{bwmeta1.element.bwnjournal-article-smv113i2p109bwm,
author = {Wies\l aw Cupa\l a},
title = {The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms},
journal = {Studia Mathematica},
volume = {113},
year = {1995},
pages = {109-125},
zbl = {0835.35101},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-smv113i2p109bwm}
}
Cupała, Wiesław. The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms. Studia Mathematica, Tome 113 (1995) pp. 109-125. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-smv113i2p109bwm/
[00000] [1] K. L. Chung, Lectures from Markov Processes to Brownian Motion, Springer, 1982. | Zbl 0503.60073
[00001] [2] W. Cupała, On the essential spectrum and eigenvalue asymptotics of certain Schrödinger operators, Studia Math. 96 (1990), 196-202. | Zbl 0716.35058
[00002] [3] W. Cupała, On the eigenvalue asymptotics of certain Schrödinger operators, ibid. 105 (1993), 101-104. | Zbl 0811.35024
[00003] [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. | Zbl 0362.47006
[00004] [5] C. L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206. | Zbl 0526.35080
[00005] [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. | Zbl 0443.35082
[00006] [7] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207. | Zbl 0312.35026
[00007] [8] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, 1980. | Zbl 0422.31007
[00008] [9] Y. Guivarc'h, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973), 333-379. | Zbl 0294.43003
[00009] [10] L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 192-218. | Zbl 0164.13201
[00010] [11] E. Lieb, The number of bound states of one-body Schrödinger operators and the Weyl problem, unpublished. | Zbl 0445.58029
[00011] [12] K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216. | Zbl 0008.11301
[00012] [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, 1979. | Zbl 0405.47007
[00013] [14] G. V. Rosenblum, The distribution of the dicrete spectrum of singular differential operators, Dokl. Akad. Nauk SSSR 202 (1972), 1012-1015 (in Russian).
[00014] [15] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1977), 247-320. | Zbl 0346.35030
[00015] [16] N. T. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260. | Zbl 0608.47047
[00016] [17] N. T. Varopoulos, Analysis on Lie groups, ibid. 76 (1988), 346-410. | Zbl 0634.22008