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Representation of functions as the Post-Widder inversion operator of generalized functions

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  • R. P. Manandhar
  • L. Debnath

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 r th 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.

Suggested Citation

  • R. P. Manandhar & L. Debnath, 1984. "Representation of functions as the Post-Widder inversion operator of generalized functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 7, pages 1-26, January.
    • Handle: RePEc:hin:jijmms:952794
    DOI: 10.1155/S0161171284000399
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