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.

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.

Shakedown in Frictional Contact Problems

2007 ◽  
Author(s):  
J. R. Barber ◽  
A. Klarbring ◽  
M. Ciavarella
Keyword(s):  
Frictional Contact ◽  
Elastic System ◽  
Contact Problems ◽  
Sufficient Condition ◽  
Normal Contact ◽  
Linear Elastic ◽  
Periodic Loading ◽  
Continuum Formulation ◽  
Complete Contact ◽  
The Continuum

If a linear elastic system with frictional interfaces is subjected to periodic loading, any slip which occurs generally reduces the tendency to slip during subsequent cycles and in some circumstances the system ‘shakes down’ to a state without slip. It has often been conjectured that a frictional Melan’s theorem should apply to this problem — i.e. that the existence of a state of residual stress sufficient to prevent further slip is a sufficient condition for the system to shake down. Here we discuss recent proofs that this is indeed the case for ‘complete’ contact problems if there is no coupling between relative tangential displacements at the interface and the corresponding normal contact tractions. By contrast, when coupling is present, the theorem applies only for a few special two-dimensional discrete cases. Counter-examples can be generated for all other cases. These results apply both in the discrete and the continuum formulation.

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.

SOLUTION OF INTEGRAL EQUATIONS BY BESSEL WAVELET TRANSFORM

2021 ◽  
Vol 10 (4) ◽  
pp. 2245-2253
Author(s):  
C. P. Pandey ◽  
P. Phukan ◽  
K. Moungkang
Keyword(s):  
Integral Equation ◽  
Wavelet Transform ◽  
Integral Equations ◽  
Volterra Integral Equation ◽  
Stable Solution ◽  
Generalized Convolution ◽  
Science And Engineering ◽  
Hankel Convolution ◽  
Distribution Spaces ◽  
Wavelet Methods

The integral equations of the first kind arise in many areas of science and engineering fields such as image processing and electromagnetic theory. The wavelet transform technique to solve integral equation allows the creation of very fast algorithms when compared with known algorithms. Various wavelet methods are used to solve certain type of integral equations. To find the most accurate and stable solution of the integral equation Bessel wavelet is the appropriate method. To study the properties of solution of integral equations on distribution spaces Bessel wavelet transform is also used. In this paper, we accomplished the concept of Hankel convolution and continuous Bessel wavelet transform to solve certain types of integral equations (Volterra integral equation of first kind, Volterra integral equation of second kind and Abel integral equation). Also distributional wavelet transform and generalized convolution will be applied to find the solution of certain Integral equations.

scholarly journals A self-reciprocal function

1939 ◽  
Vol 6 (2) ◽  
pp. 92-93
Author(s):  
Brij Mohan
Keyword(s):  
Hankel Transform ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Order Zero ◽  
Image Position ◽  
Necessary And Sufficient

1. The object of this note is to discover a new function which is its own reciprocal in the Hankel Transform of order zero.I will make use of the following theorem of Hardy and Titchmarsh1:–A necessary and sufficient condition that a Junction f (x) should be its own Jv transform is that it should be of the formwhere 0 < c < 1, and

Seismic Reservoir Delineation via Hankel Transform Based Enhanced Empirical Wavelet Transform

2020 ◽  
Vol 17 (8) ◽  
pp. 1411-1414
Author(s):  
Hui Li ◽  
Jing Lin ◽  
Naihao Liu ◽  
Fangyu Li ◽  
Jinghuai Gao
Keyword(s):  
Wavelet Transform ◽  
Hankel Transform ◽  
Empirical Wavelet Transform ◽  
Seismic Reservoir

scholarly journals Bessel wavelet transform on the spaces with exponential growth

Filomat ◽  
2017 ◽  
Vol 31 (8) ◽  
pp. 2459-2466 ◽  
Author(s):  
S.K. Upadhyay ◽  
Reshma Singh
Keyword(s):  
Integral Equation ◽  
Wavelet Transform ◽  
Exponential Growth ◽  
Hankel Transform ◽  
Fredholm Type ◽  
Type Spaces

The Bessel wavelet transform on Xu and Qu type spaces of exponential growth are investigated and their properties discussed by using the theory of the Hankel transform. Using this said theory, the integral equation of Fredholm type is defined and some examples associated with this integral equation are given.

scholarly journals About calculation of the Hankel transform using preliminary wavelet transform

2003 ◽  
Vol 2003 (6) ◽  
pp. 319-325 ◽  
Author(s):  
E. B. Postnikov
Keyword(s):  
Wavelet Transform ◽  
Numerical Evaluation ◽  
Hankel Transform ◽  
Input Function ◽  
Analytical Representation ◽  
Wavelet Coefficients ◽  
Test Function ◽  
Struve Functions

The purpose of this paper is to present an algorithm for evaluating Hankel transform of the null and the first kind. The result is the exact analytical representation as the series of the Bessel and Struve functions multiplied by the wavelet coefficients of the input function. Numerical evaluation of the test function with known analytical Hankel transform illustrates the proposed algorithm.

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