Substitution theorems for integral transforms with symmetric kernels
type: Item
instance of: scholarly article
title: Substitution theorems for integral transforms with symmetric kernels
zbMATH Open document ID: 0652.44002
author: K. C. Gupta
author: S. M. Agrawal
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 1988-01-01T00:00:00Z
review text: The authors deduce a number of general theorems for a class of integral transforms. If we use the notation \[ h(p)=T\{f(x);p\}=\int^{\infty}_{0}K(p,x)f(x)dx \] and \(h(p;(b,c))=T\{f(x)[U(x-b)-U(x-c)];p\}=\int^{c}_{b}K(p,x)f(x)dx\) then one of the theorems proved by the authors is: If \(h_ 1(p)=T_ 1\{k(x)h_ 2[g(x)];p\}\) and \(h_ 2(p^{\sigma})=T_ 2\{f(x);p\}\) then \(h_ 1(p)=\sigma \int^{\infty}_{0}\phi (p,u)f(u)du\) where \[ \phi (p,u)=T_ 2\{K_ 1[ph(y^{\sigma})K[h(y^{\sigma})]y^{\sigma - 1}h'(y^{\sigma});u\}. \] Suitable special cases are mentioned.
Mathematics Subject Classification ID: 44A05
zbMATH DE Number: 4063766
zbMATH Keywords: substitution theorems
zbMATH Keywords: symmetric kernels
zbMATH Keywords: Fourier cosine transform
reviewed by: R. P. Agarwal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4063766