Index integral transformations of Titchmarsh type

• Type: Article in International Scientific Journal
• Date: 1997

Authors

Yakubovich, SB (Author) Other

Journal

Title: Journal of Computational and Applied Mathematics

Vol. 85

Pages: 169-179

ISSN: 0377-0427

Publisher: Elsevier

Indexing

ISI Web of Knowledge

Scopus - 6 Citations

Other information

Authenticus ID: P-007-7T1

Abstract (EN): In 1946 Titchmarsh [4] introduced the integral transformation g(¿)= (latin small letter esh)¿0 ReJi¿(x)f(x)dx, which depends on the index of a Bessel function, in connection with a continuous spectral Bessel function expansion in Sturm-Liouville boundary value problems. Here, we generalize this transformation by using the composition properties and a relationship with the Kontorovich-Lebedev and the Mellin-type transformations, and we give a variety of index transformations with a linear combination depending on a parameter of real and imaginary parts of a Bessel function. As it is shown the inversion formula consists of the integral over the index of a Lommel function.

Language: English

Type (Professor's evaluation): Scientific