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• W2953233947 abstract "In this article we prove the equivalence of certain inequalities for Riesz means of eigenvalues of the Dirichlet Laplacian with a classical inequality of Kac. Connections are made via integral transforms including those of Laplace, Legendre, Weyl, and Mellin, and the Riemann-Liouville fractional transform. We also prove new universal eigenvalue inequalities and monotonicity principles for Dirichlet Laplacians as well as certain Schrodinger operators. At the heart of these inequalities are calculations of commutators of operators, sum rules, and monotonic properties of Riesz means. In the course of developing these inequalities we prove new bounds for the partition function and the spectral zeta function (cf. Corollaries 3.5-3.7) and conjecture about additional bounds." @default.
• W2953233947 created "2019-06-27" @default.
• W2953233947 creator A5002828363 @default.
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• W2953233947 date "2007-12-25" @default.
• W2953233947 modified "2023-09-27" @default.
• W2953233947 title "On Riesz Means of Eigenvalues" @default.
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• W2953233947 hasPublicationYear "2007" @default.
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