On the spectrum of two different fractional operators

Raffaella Servadei, Enrico Valdinoci

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133 Citations (Scopus)

Abstract

In this paper we deal with two non-local operators that are both well known and widely studied in the literature in connection with elliptic problems of fractional type. More precisely, for a fixed s ∈ (0,1) we consider the integral definition of the fractional Laplacian given by where c(n, s) is a positive normalizing constant, and another fractional operator obtained via a spectral definition, that is, where e i, λ i are the eigenfunctions and the eigenvalues of the Laplace operator -Δ in Ω with homogeneous Dirichlet boundary data, while a i represents the projection of u on the direction e i. The aim of this paper is to compare these two operators, with particular reference to their spectrum, in order to emphasize their differences.

Original languageEnglish
Pages (from-to)831-855
Number of pages25
JournalProceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume144
Issue number4
DOIs
Publication statusPublished - 1 Jan 2014
Externally publishedYes

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