New inversion, convolution and Titchmarsh's theorems for the half-Hilbert transform

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Yakubovich, S (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Vol. 25

Pages: 955-968

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 3 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-009-W7Z

DOI: 10.1080/10652469.2014.949257

Abstract (EN): While exploiting the generalized Parseval equality for the Mellin transform, we derive the reciprocal inverse operator in the weighted L-2-space related to the Hilbert transform on the nonnegative half-axis. Moreover, employing the convolution method, which is based on the Mellin-Barnes integrals, we prove the corresponding convolution and Titchmarsh's theorems for the half-Hilbert transform. Some applications to the solvability of a new class of singular integral equations are demonstrated. Our technique does not require the use of methods of the Riemann-Hilbert boundary value problems for analytic functions. The same approach is applied recently to invert the half-Hartley transform and to establish its convolution theorem.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14