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Essential spectra of elliptic partial differential equations

Name: Essential spectra of elliptic partial differential equations
Creator: Schechter, Martin
Keywords: functional analysis

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 1967Publisher:American Mathematical Society (AMS)Journal:Bulletin of the American Mathematical Society, volume 73, pages 567-572 (issn: 0273-0979, eissn: 1088-9485,

Authors: Schechter, Martin;

doi: 10.1090/s0002-9904-1967-11752-x

Essential spectra of elliptic partial differential equations

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Abstract

Let A be a closed, densely defined operator in a Banach space X. There are several definitions of the "essential" spectrum of A (cf. [ l ] , [2]). According to Wolf [3], [4] it is the complement in the complex plane of the $-set of A. The $-set $A of A is the set of points X for which (a) a(A — X), the dimension of the null space of A — X, is finite (b) R(A —X), the range of A —X, is closed (c) p(A •—X), the codimension of R(^4 — X), is finite. We denote the essential spectrum according to this definition by dew{A). The set crem(A)f as defined in [ l ] , [2] is obtained by adding to

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functional analysis

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