New index transforms of the Lebedev-Skalskaya type

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Yakubovich, SB (Author) FCUP

Journal

Title: Integral Transforms and Special Functions

Vol. 27 No. 2

Pages: 137-152

ISSN: 1065-2469

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 3 Citations

Other information

Authenticus ID: P-00K-0HW

DOI: 10.1080/10652469.2015.1098637

Abstract (EN): New index transforms, involving the real part of the modified Bessel function of the first kind as the kernel are considered. Mapping properties such as the boundedness and invertibility are investigated for these operators in the Lebesgue spaces. Inversion theorems are proved. As an interesting application, a solution of the initial value problem for the second-order partial differential equation, involving the Laplacian, is obtained. It is noted that the corresponding operators with the imaginary part of the modified Bessel function of the first kind lead to the familiar Kontorovich-Lebedev transform and its inverse.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16