Functional inequalities and spectrum estimates: The infinite measure case (Q1865303)

The paper is a continuation of the author's paper [ibid. 170, 219-245 (2000; Zbl 0946.58010)] providing a modification of the super-Poincaré inequality so that the infimum of the essential spectrum is well described even if the reference measure is infinite. Higher-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. Some concrete examples are considered to illustrate the main results. In particular, estimates of higher-order eigenvalues obtained in the paper are sharp as checked by examples on the Euclidean space.