The Journal of the Indian Mathematical Society

R. S. Pathak ¹

Affiliations
1 DST Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi 221005, IN

Abstract

Moment asymptotic expansions of the n-dimensional wavelet transform are obtained for large values of the dilation parameter a. Using representation of the n-dimensional wavelet transform as a 2n-dimensional Fourier transform asymptotic expansion of the wavelet transform with explicit error bound is also obtained. Results are illustrated by means of suitable examples.

Keywords

Asymptotic Expansion, Wavelet Transform, Fourier Transform, Error Bound.

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R. S. Pathak ¹

Affiliations
1 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 S_α' (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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R. S. Pathak ¹, S. M. Tripathi ¹

Affiliations
1 Department of Mathematics, Banaras Hindu University, Varanasi-221005, IN

Abstract

A pseudo-differential operator h_μ^v_a involving Hankel transforms, which maps the Zemanian space H_μ into H_v, is defined. An integral representation for h_μ^v_a is given and an L¹-boundedness result is obtained.

Keywords

Pseudo-Differential Operator, Hankel Transform, Hankel Convolution.

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R. S. Pathak ¹, A. C. Paul ¹

Affiliations
1 Department of Mathematics, Banaras Hindu University, Varanasi 221 005, IN

Abstract

Ultradistributions are represented as boundary values of analytic functions and structure theorems of ultradistributions are given by Komatsu [7].

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