Title

Recent Developments On The Stieltjes Transform Of Generalized Functions

Keywords

Abelian theorems; Final-value and initial-value results; fractional order integration; hyper-geometric transform; Kernel and adjoint methods; Laplace transforms; Poisson transforms; Real and complex inversion theorems; Stieltjes transforms of ordinary and generalized functions; Weyl fractional integral

Abstract

This paper is concerned with recent developments on the Stieltjes transform of generalized functions. Sections 1 and 2 give a very brief introduction to the subject and the Stieltjes transform of ordinary functions with an emphasis to the inversion theorems. The Stieltjes transform of generalized functions is described in section 3 with a special attention to the inversion theorems of this transform. Sections 4 and 5 deal with the adjoint and kernel methods used for the development of the Stieltjes transform of generalized functions. The real and complex inversion theorems are discussed in sections 6 and 7. The Poisson transform of generalized functions, the iteration of the Laplace transform and the iterated Stieltjes transfrom are included in sections 8, 9 and 10. The Stieltjes transforms of different orders and the fractional order integration and further generalizations of the Stieltjes transform are discussed in sections 11 and 12. Sections 13, 14 and 15 are devoted to Abelian theorems, initial-value and final-value results. Some applications of the Stieltjes transforms are discussed in section 16. The final section deals with some open questions and unsolved problems. Many important and recent references are listed at the end. © 1987, Hindawi Publishing Corporation. All rights reserved.

Publication Date

1-1-1987

Publication Title

International Journal of Mathematics and Mathematical Sciences

Volume

10

Issue

4

Number of Pages

641-670

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1155/S0161171287000784

Socpus ID

0344871254 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/0344871254

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