On a testing-function space for distributions associated with the Kontorovich-Lebedev transform

• Type: Article in International Scientific Journal
• Date: 2006

Authors

Semyon B Yakubovich (Author) FCUP

Journal

Title: Collectanea Mathematica

Vol. 57

Pages: 279-293

ISSN: 0010-0757

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 6 Citations

Scopus - 5 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-004-PBV

Abstract (EN): We construct a testing-function space, which is equipped with the topology that is generated by L-nu,L-p - multinorm of the differential operator A(x) = x(2) - x d/dx [x d/dx], and its k-th iterates A(x)(k), where k = 0, 1, and A(x)(0) phi = phi. Comparing with other testing-function spaces, we introduce in its dual the Kontorovich-Lebedev transformation for distributions with respect to a complex index. The existence, uniqueness, imbedding and inversion properties are investigated. As an application we find a solution of the Dirichlet problem for a wedge for the harmonic type equation in terms of the Kontorovich-Lebedev integral.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 15