On the generalized Lebedev index transform

• Type: Article in International Scientific Journal
• Date: 2015

Authors

Yakubovich, SB (Author) FCUP

Journal

Title: Journal of Mathematical Analysis and Applications

Vol. 429 No. 1

Pages: 184-203

ISSN: 0022-247X

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 1 Citation

Scopus - 1 Citation

Other information

Authenticus ID: P-00G-45K

DOI: 10.1016/j.jmaa.2015.04.017

Abstract (EN): An essential generalization of the Lebedev index transform with the square of the Macdonald function is investigated. Namely, we consider a family of integral operators with the positive kernel vertical bar K(ir+alpha)/2(x)vertical bar(2), alpha is an element of R, x > 0, T E R, where K-mu(z) is the Macdonald function and i is the imaginary unit. Mapping properties such as the boundedness, compactness, invertibility are investigated for these operators and their adjoints in weighted L-p spaces. Inversion theorems are proved. Important particular cases are exhibited. As an interesting application, a solution of the initial value problem for the second order differential difference equation, involving the Laplacian, is obtained.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 20