This is a preview of subscription content, log in via an institution to check access.
References
M. Sh. Birman,On the spectrum of singular boundary-value problems, Mat. Sbornik55 (1961), 125–174. (Russian)
M. Sh. Birman and M. Z. Solomyak,Quantitive analysis in Sobolev imbedding theorems and applications to spectral theory, Tenth Mathematical School, Izd. Inst. Mat. Akad. Nauk Ukrain. SSSR, Kiev, 1974, pp. 5–189 (Russian); English transl, in Amer. Math. Soc. Transi. (2)114 (1980), 1–132.
M. Sh. Birman and M. Z. Solomyak,Estimates for the number of negative eigenvalues of the Schrödinger operator and its generalizations, Advances in Soviet Math.7 (1991), 1–55.
J. P. Conlon,A new proof of the Cwikel-Lieb-Rosenbljum bound, Rocky Mountain J. Math.15 (1985), 117–122.
W. Cupala,The upper bound of the number of eigenvalues for a class of perturbed Dirichlet forms, Studia Math.113 (2) (1995), 109–125.
M. Cwikel,Weak type estimates for singular values and the number of bound states of Schrödinger operators, Ann. of Math. (2)106 (1977), 93–100.
E. B. Davies,Heat Kernels and Spectral Theory, Cambridge University Press, Cambridge, 1989.
E. Hebey,Optimal Sobolev inequalities on complete Riemannian manifolds with Ricci curvature bounded below and positive injectivity radius, Amer. J. Math.118 (1996), 291–300.
P. Li and S-T. Yau,On the Schrödinger equation and the eigenvalue problem, Comm. Math. Phys.88 (1983), 309–318.
E. Lieb,Bounds on the eigenvalues of the Laplace and Schrödinger operators, Bull. Amer. Math. Soc.82 (1976), 751–753.
V. Liskevich and Yu. Semenov,Some problems on Markov semigroups, inAdvances in Partial Differential Equations, Akademie Verlag, Berlin, 1996 (in press).
V. G. Maz’ya,Sobolev spaces, Izdat. Leningr. Univ., Leningrad, 1985 (Russian); English transi.: Springer-Verlag, Berlin, 1985.
G. V. Rozenblyum,The distribution of the discrete spectrum for singular differential operators, Dokl. Akad. Nauk SSSR202 (1972), 1012–1015. (Russian).
B. Simon,Weak trace ideals and number of bound states of Schrödinger operator, Trans. Amer. Math. Soc.224 (1976), 367–380.
M. Solomyak,On the negative discrete spectrum of the operator δN — αVfor a class of unbounded domains in Rd, inProc. of the Conference in PDE, Toronto, 1996 (in press).
N. Th. Varopoulos,Small time Gaussian estimates of heat diffusion kernels. Part I: The semigroup technique, Bull. Sci. Math.113 (1989), 253–277.
N. Th. Varopoulos, L. Saloff-Coste and T. Coulhon,Analysis and Geometry on Groups, Cambridge University Press, Cambridge, 1992.
A. C. Zaanen,Riesz Spaces II, North-Holland, Amsterdam-New York-Oxford, 1983.
Author information
Authors and Affiliations
Corresponding author
Additional information
Partially supported by a Research Grant from the Cemach and Anna Oiserman Research Fund.
Rights and permissions
About this article
Cite this article
Levin, D., Solomyak, M. The rozenblum-lieb-cwikel inequality for markov generators. J. Anal. Math. 71, 173–193 (1997). https://doi.org/10.1007/BF02788029
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02788029