ABSTRACT

For those who have a background in advanced calculus, elementary topology and functional analysis - from applied mathematicians and engineers to physicists - researchers and graduate students alike - this work provides a comprehensive analysis of the many important integral transforms and renders particular attention to all of the technical aspects of the subject. The author presents the last two decades of research and includes important results from other works.

chapter 1|32 pages

Normed and Countably Normed Spaces

chapter 2|40 pages

Fourier Transforms of Distributions

chapter 3|45 pages

Fourier Transforms of Ultradistributions

chapter 4|31 pages

Laplace Transform

chapter 5|34 pages

Stieltjes Transform

chapter 6|26 pages

Hilbert Transform

chapter 7|27 pages

Mellin and Watson Transforms

chapter 8|43 pages

Hankel Transforms of Distributions

chapter 9|35 pages

Hankel Transforms of Ultradistributions

chapter 10|24 pages

Kontorovich–Lebedev Transform

chapter 11|24 pages

Generalized Mehler–Fock Transform