Eigenfunction of the Laplacian as a Degenerate Case of a Function with its Fourier Transform Supported in an Annulus
Rudra P. Sarkar
Indian Statistical Institute, Kolkata, India
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Abstract
The aim of this paper is to reach a characterization of the eigenfunction of the Laplace–Beltrami operator as a degenerate case of the inverse Paley–Wiener theorem (for functions whose Fourier transform is supported on a compact annulus) on the rank-1 Riemannian symmetric spaces of noncompact type. The most distinguished prototypes of these spaces are the hyperbolic spaces.
Cite this article
Rudra P. Sarkar, Eigenfunction of the Laplacian as a Degenerate Case of a Function with its Fourier Transform Supported in an Annulus. Publ. Res. Inst. Math. Sci. 54 (2018), no. 2, pp. 351–378
DOI 10.4171/PRIMS/54-2-4