Lower Bounds on the Number of Points in the Lower Spectrum of Elliptic Operators

Allegretto, Walter

Canadian journal of mathematics, Tome 31 (1979) no. 2, pp. 419-426

Résumé

Let G denote an unbounded domain of Euclidean m-space Em with regular boundary, and let L be a self-adjoint operator generated in L 2 (G) by a second order elliptic expression. We denote by S(L) the spectrum of L, by μ the least point of the essential spectrum Se(L) and by N(L) the number of bound states of L; that is, the number of points in (–∞, μ) ∩ S(L). There are many results in the literature dealing with the localization, significance and properties of μ, of Se (L) and of (–∞, μ)⌒ S(L), with most of the emphasis on the cases where G = Em or G is the exterior of a closed surface in Em. We refer the reader to the books by Glazman [12], Schechter [19], Reed and Simon [18], and Paris [9], where extensive references are also found.

Détail

DOI : 10.4153/CJM-1979-045-0

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