✦ LIBER ✦

Index integral transformations of Titchmarsh type

✍ Scribed by S.B. Yakubovich

Book ID: 104338496
Publisher: Elsevier Science
Year: 1997
Tongue: English
Weight: 437 KB
Volume: 85
Category: Article
ISSN: 0377-0427
DOI: 10.1016/s0377-0427(97)00143-x

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✦ Synopsis

In 1946 Titchmarsh [4] introduced the integral transformation f0 °°

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.

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The Aim Of This Book Is To Develop A New Approach Which We Called The Hyper Geometric One To The Theory Of Various Integral Transforms, Convolutions, And Their Applications To Solutions Of Integro-differential Equations, Operational Calculus, And Evaluation Of Integrals. We Hope That This Simple App