The Journal of the Indian Mathematical Society

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A Representation Theorem for a Class of Stieltjes Transformable Generalized Functions


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1 Department of Mathematics, Banaras Hindu University, Varanasi-221005, India
     

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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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  • A Representation Theorem for a Class of Stieltjes Transformable Generalized Functions

Abstract Views: 173  |  PDF Views: 0

Authors

R. S. Pathak
Department of Mathematics, Banaras Hindu University, Varanasi-221005, India

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.