A Representation Theorem for a Class of Stieltjes Transformable Generalized Functions
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.Downloads
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Copyright (c) 1974 R. S. Pathak
This work is licensed under a Creative Commons Attribution 4.0 International License.
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).