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

• Autorzy: Wiesław Cupała
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

eigenvalue asymptotics; Dirichlet form; Markov process; Lie group

Kategorie tematyczne

• 35Hxx: Close-to-elliptic equations and systems

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1995
• Tom: 113
• Numer: 2
• Strony: 109-125

Daty

wydano

1995

otrzymano

1993-08-19

poprawiono

1994-07-25

Twórcy

autor

Wiesław Cupała

• Institute of Mathematics, Polish Academy of Sciences, Wrocław Branch, Kopernika 18, 51-617 Wrocław, Poland

Bibliografia

• [1] K. L. Chung, Lectures from Markov Processes to Brownian Motion, Springer, 1982.
• [2] W. Cupała, On the essential spectrum and eigenvalue asymptotics of certain Schrödinger operators, Studia Math. 96 (1990), 196-202.
• [3] W. Cupała, On the eigenvalue asymptotics of certain Schrödinger operators, ibid. 105 (1993), 101-104.
• [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.
• [5] C. L. Fefferman, The uncertainty principle, Bull. Amer. Math. Soc. 9 (1983), 129-206.
• [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.
• [7] G. B. Folland, Subelliptic estimates and function spaces on nilpotent Lie groups, Ark. Mat. 13 (1975), 161-207.
• [8] M. Fukushima, Dirichlet Forms and Markov Processes, North-Holland, 1980.
• [9] Y. Guivarc'h, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973), 333-379.
• [10] L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 192-218.
• [11] E. Lieb, The number of bound states of one-body Schrödinger operators and the Weyl problem, unpublished.
• [12] K. Löwner, Über monotone Matrixfunktionen, Math. Z. 38 (1934), 177-216.
• [13] M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vol. 4, Academic Press, 1979.
• [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] L. P. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1977), 247-320.
• [16] N. T. Varopoulos, Hardy-Littlewood theory for semigroups, J. Funct. Anal. 63 (1985), 240-260.
• [17] N. T. Varopoulos, Analysis on Lie groups, ibid. 76 (1988), 346-410.