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International Journal of Mathematics and Mathematical Sciences
Volume 8 (1985), Issue 4, Pages 719-723
http://dx.doi.org/10.1155/S0161171285000801

On two new characterizations of Steiltjes transforms for distributions

Department of Mathematics, Tata College Chaibasa, Singhbhum, Bihar 833202, India

Received 27 September 1981

Copyright © 1985 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Two new characterizations of the Stieltjes transform for distribution are developed, using two transformations on the space of distributions viz., dilation Un and exponential shifts Tp. The standard theorem on analyticity, uniqueness and invertibility of the Stieltjes transform are proved, using the new characterization as the definition of the Stieltjes transform.