Special Function Potentials for the Laplacian

Fegan, H. D.

Canadian journal of mathematics, Tome 34 (1982) no. 5, pp. 1183-1194

Résumé

The purpose of this paper is to study the operator Δ + q. Here Δ is the Laplace–Beltrami operator on a compact Lie group G and q is a matrix coefficient of a representation of G. We are able to calculate the powers of Δ + q acting on the function qku. This is done in Section 2 and the reader is refered there for definitions of the special functions q and u.The interest in the operator Δ + q comes originally from physics and in particular from the Schrödinger equation. This is described in [4]. Here we are restricting ourselves to mathematical questions and shall not consider any applications to physics.In this paper we take the heat equation with potential as (1.1) with , the upper half plane, and initial data f(x, 0) = qk (x)u(x).

Détail

DOI : 10.4153/CJM-1982-081-3

Bibliographie

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