scholarly journals Calderón's reproducing formula for Hankel convolution

2006 ◽  
Vol 2006 ◽  
pp. 1-7 ◽  
Author(s):  
R. S. Pathak ◽  
Gireesh Pandey
Keyword(s):  
Hankel Transform ◽  
Calderón’S Reproducing Formula ◽  
Hankel Convolution

Calderón-type reproducing formula for Hankel convolution is established using the theory of Hankel transform.

The relation between Bessel wavelet convolution product and Hankel convolution product involving Hankel transform

2017 ◽  
Vol 15 (04) ◽  
pp. 1750030 ◽  
Author(s):  
S. K. Upadhyay ◽  
Reshma Singh ◽  
Alok Tripathi
Keyword(s):  
Wavelet Transform ◽  
Hankel Transform ◽  
Convolution Product ◽  
Hankel Transformation ◽  
Hankel Convolution ◽  
Transform Approximation

In this paper, the relation between Bessel wavelet convolution product and Hankel convolution product is obtained by using the Bessel wavelet transform and the Hankel transform. Approximation results of the Bessel wavelet convolution product are investigated by exploiting the Hankel transformation tool. Motivated from the results of Pinsky, heuristic treatment of the Bessel wavelet transform is introduced and other properties of the Bessel wavelet transform are studied.

Integrability of the continuum Bessel wavelet kernel

2015 ◽  
Vol 13 (05) ◽  
pp. 1550032 ◽  
Author(s):  
S. K. Upadhyay ◽  
Reshma Singh
Keyword(s):  
Wavelet Transform ◽  
Hankel Transform ◽  
Sufficient Condition ◽  
Hankel Convolution ◽  
The Continuum

In this paper, the sufficient condition for the integrability of the kernel of the inverse Bessel wavelet transform is obtained by using the theory of Hankel transform and Hankel convolution.

On the surjectivity of Hankel convolution operators on Beurling-type distribution spaces

2005 ◽  
Vol 135 (3) ◽  
pp. 479-512
Author(s):  
M. Belhadj ◽  
J. J. Betancor
Keyword(s):  
Convolution Operator ◽  
Differential Operators ◽  
Structure Theorem ◽  
Sufficient Conditions ◽  
Hankel Transform ◽  
Convolution Operators ◽  
Type Distribution ◽  
Hankel Convolution ◽  
Distribution Spaces ◽  
Necessary And Sufficient

In this paper we consider Beurling-type distributions in the Hankel setting. The Hankel transform and Hankel convolution are studied on Beurling-type distributions. We also introduce a class of ultra-differential operators that allows us to show a Hankel version of the second structure theorem of Komatsu and Braun. Necessary and sufficient conditions are established in order that a Beurling distribution generates a surjective Hankel convolution operator.

On the surjectivity of Hankel convolution operators on Beurling-type distribution spaces

2005 ◽  
Vol 135 (3) ◽  
pp. 479-512
Author(s):  
M. Belhadj ◽  
J. J. Betancor
Keyword(s):  
Convolution Operator ◽  
Differential Operators ◽  
Structure Theorem ◽  
Sufficient Conditions ◽  
Hankel Transform ◽  
Convolution Operators ◽  
Type Distribution ◽  
Hankel Convolution ◽  
Distribution Spaces ◽  
Necessary And Sufficient

In this paper we consider Beurling-type distributions in the Hankel setting. The Hankel transform and Hankel convolution are studied on Beurling-type distributions. We also introduce a class of ultra-differential operators that allows us to show a Hankel version of the second structure theorem of Komatsu and Braun. Necessary and sufficient conditions are established in order that a Beurling distribution generates a surjective Hankel convolution operator.

Some Properties of Hankel Convolution Operators

1993 ◽  
Vol 36 (4) ◽  
pp. 398-406 ◽  
Author(s):  
J. J. Betancor ◽  
I. Marrero
Keyword(s):  
Sufficient Conditions ◽  
Hankel Transform ◽  
Generalized Functions ◽  
Necessary And Sufficient Conditions ◽  
Convolution Operators ◽  
Zemanian Space ◽  
Hankel Convolution ◽  
Necessary And Sufficient

AbstractLet be the Zemanian space of Hankel transformable generalized functions and let be the space of Hankel convolution operators for . This is the dual of a subspace of for which is also the space of Hankel convolutors. In this paper the elements of are characterized as those in and in that commute with Hankel translations. Moreover, necessary and sufficient conditions on the generalized Hankel transform are established in order that every such that in .

Titchmarsh's theorem of Hankel transform

2019 ◽  
pp. 11-24
Author(s):  
Mohamed-Ahmed Boudref
Keyword(s):  
Number Theory ◽  
Data Analysis ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Lipschitz Condition ◽  
Analytic Number Theory ◽  
Hankel Transform ◽  
Partial Differential ◽  
Analytic Number ◽  
Bessel Transform

Hankel transform (or Fourier-Bessel transform) is a fundamental tool in many areas of mathematics and engineering, including analysis, partial differential equations, probability, analytic number theory, data analysis, etc. In this article, we prove an analog of Titchmarsh's theorem for the Hankel transform of functions satisfying the Hankel-Lipschitz condition.

scholarly journals Interior-stress fields produced by a general axisymmetric punch

Friction ◽  
2021 ◽  
Author(s):  
Longxiang Yang ◽  
Zhanjiang Wang ◽  
Weiji Liu ◽  
Guocheng Zhang ◽  
Bei Peng
Keyword(s):  
Hankel Transform ◽  
Elastic Half Space ◽  
Stress Fields ◽  
Dual Integral Equations ◽  
Total Load ◽  
Interior Stress ◽  
Von Mises ◽  
Von Mises Stresses ◽  
Relationship Of ◽  
Analytical Expressions

AbstractThis work is a supplement to the work of Sneddon on axisymmetric Boussinesq problem in 1965 in which the distributions of interior-stress fields are derived here for a punch with general profile. A novel set of mathematical procedures is introduced to process the basic elastic solutions (obtained by the method of Hankel transform, which was pioneered by Sneddon) and the solution of the dual integral equations. These processes then enable us to not only derive the general relationship of indentation depth D and total load P that acts on the punch but also explicitly obtain the general analytical expressions of the stress fields beneath the surface of an isotropic elastic half-space. The usually known cases of punch profiles are reconsidered according to the general formulas derived in this study, and the deduced results are verified by comparing them with the classical results. Finally, these general formulas are also applied to evaluate the von Mises stresses for several new punch profiles.

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