A Representation Theorem for a Class of Stieltjes Transformable Generalized Functions

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Authors

  • Department of Mathematics, Banaras Hindu University, Varanasi-221005 ,IN

Abstract

The classical Stieltjes transform has recently been extended to a certain class of generalized functions Sα' (I) by Pandey [1], and the real and complex inversion formulae [3, pp. 126, 144] have been shown to be still valid when the limiting operation in those formulae is understood as weak convergence in the space D'{I) of Schwartz distributions.

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Published

1974-12-01

How to Cite

Pathak, R. S. (1974). A Representation Theorem for a Class of Stieltjes Transformable Generalized Functions. The Journal of the Indian Mathematical Society, 38(1-4), 339–344. Retrieved from https://informaticsjournals.com/index.php/jims/article/view/16709

 

References

PANDEY, J. N., On the Stieltjes transform of generalized functions, Proc. Camb. Phil. Soc, 71 (1972), 85-96.

TREVES, F., Topological vector spaces, distributions and kernels. Academic Press New York (1967).

WIDDER, D. V., An introduction to transform theory, Academic Press, (1971).

ZEMANIAN, A. H., Generalized integral transformations, Interscience Publishers (1968).