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Sur quelques opérateurs liés à l’équation de Helmholtz en coordonnées polaires, transformation H.K.L. (Hankel-Kantorovich- Lebedev). (On some operators for the Helmholtz equation in polar coordinates, H.K.L. transform). (French) Zbl 0694.35040
Summary: We give here the properties of two operators \(A_+\) and \(A_-\) related to the Helmholtz equation with the Sommerfeld radiation conditions. The properties of the (Hankel)-Kantorovich-Lebedev transform are obtained by the diagonalization of two operators \(A_{\pm}\).

MSC:
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35A22 Transform methods (e.g., integral transforms) applied to PDEs
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