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标题：Representation of functions as the Post-Widder inversion operator of generalized functions
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作者：R. P. Manandhar ; L. Debnath
期刊名称：International Journal of Mathematics and Mathematical Sciences
印刷版ISSN：0161-1712
电子版ISSN：1687-0425
出版年度：1984
卷号：7
DOI：10.1155/S0161171284000399
出版社：Hindawi Publishing Corporation
摘要：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.