Function with its Fourier transform supported on annulus and\n eigenfunction of Laplacian

2014/06/16 by Rudra P. Sarkar, Sarkar, Rudra P
Mathematics · #43A85 #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Analysis and Transform Methods #Spectral Theory in Mathematical Physics #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1406.3964

openalex publication_date 2014/06/16 · openalex created_date 2022/09/30 · openalex updated_date 2026/07/28

Abstract

We explore the possibilities of reaching the characterization of\neigenfunction of Laplacian as a degenerate case of the inverse Paley-Wiener\ntheorem (characterizing functions whose Fourier transform is supported on a\ncompact annulus) for the Riemannian symmetric spaces of noncompact type. Most\ndistinguished prototypes of these spaces are the hyperbolic spaces. The\nstatement and the proof of the main result work mutatis-mutandis for a number\nof spaces including Euclidean spaces and Damek-Ricci spaces.\n

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