Index integral transformations of Titchmarsh type

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:85

Article

Yakubovich, SB

关键词: the Titchmarsh transform;    the Kontorovich-Lebedev transform;    the Mellin transform;    Bessel functions;    Lommel functions;   

DOI  :  10.1016/S0377-0427(97)00143-X

来源: Elsevier

【 摘 要 】

In 1946 Titchmarsh [4] introduced the integral transformation g(tau) = integral(0)(infinity) ReJ(i tau)(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.

【 授权许可】

Free