Title

Representation Of Functions As The Post Widder Inversion Operator Of Generalized Functions

Keywords

generalized functions; Post-Widder inversion operator; Representation theorems; Testing function space and its dual

Abstract

A study is made of the Post-Widder inversion operator to a class of generalized functions in the sense of distributional convergence. Necessary and sufficient conditions are proved for a given function to have the representation as the rth operate of the Post-Widder inversion operator of generalized functions. Some representation theorems are also proved. Certain results concerning the testing function space and its dual are established. A fundamental theorem regarding the existence of the real inversion operator (1.6) with r = 0 is proved in section 4. A classical inversion theory for the Post-Widder inversion operator with a few other theorems which are fundamental to the representation theory is also developed in this paper. © 1984, Hindawi Publishing Corporation. All rights reserved.

Publication Date

1-1-1984

Publication Title

International Journal of Mathematics and Mathematical Sciences

Volume

7

Issue

2

Number of Pages

371-396

Document Type

Article

Personal Identifier

scopus

DOI Link

https://doi.org/10.1155/S0161171284000399

Socpus ID

84929859409 (Scopus)

Source API URL

https://api.elsevier.com/content/abstract/scopus_id/84929859409

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