Spectral measure of Laplacean operators in Paley-Wiener space

2010/05/10 by Dăng Vũ Giang, Dang Vu Giang, Giang, Dang Vu
Mathematics · #FOS: Mathematics #General Mathematics (math.GM) #Mathematical Analysis and Transform Methods #Numerical methods in inverse problems #Spectral Theory in Mathematical Physics #math.GM

paper · pdf · doi:10.48550/arxiv.1005.1438

openalex publication_date 2010/05/10 · arxiv created 2013/04/02 · arxiv updated 2013/04/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We are interested in computing the spectral measure of Laplacean operators in Paley-Wiener space, the Hilbert space of all square integrable functions having Fourier transforms supported in a compact set K, the closure of an open bounded set in \R^N. I is well-known that every differential operator is bounded in this space. Among others, we will prove that the spectrum of Laplace operator is the set \-|x|²: x∈ K\.

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