Functional Inequalities and Spectrum Estimates: The Infinite Measure Case

By Feng-Yu Wang. 2002

54 citations recorded by the source corpus.

Abstract As a continuation of [13] where a Poincare-type inequality was introduced to study the essential spectrum on the L 2 -space of a probability measure, this paper provides a modification of this inequality so that the infimum of the essential spectrum is well described even if the reference measure is infinite. High-order eigenvalues as well as the corresponding semigroup are estimated by using this new inequality. Criteria of the inequality and estimates of the inequality constants are presented. Finally, some concrete examples are considered to illustrate the main results. In particular, estimates of high-order eigenvalues obtained in this paper are sharp as checked by two examples on the Euclidean space.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/781478c35f6c643e49863f8ebca83a403ee39f81

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In Mathematical Physics

In Statistics and Probability

Citations in the corpus

Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below (2006, background): “This inequality has been applied and further developed to the study of functional inequalities (see [1,22,27,29]), heat kernel estimates (see [4,10]), higher order eigenvalues (see [11,28,30]), transportation cost inequalities (see [5]), and short time behavior of transition probabilities (see [2,3,”