Weyl transforms associated with the Hankel transform in Clifford analysis

2006 ◽  
Vol 29 (7) ◽  
pp. 839-851 ◽  
Author(s):  
Jiman Zhao ◽  
Hongbo Li
Keyword(s):  
Clifford Analysis ◽  
Hankel Transform ◽  
Weyl Transforms

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.

scholarly journals On the Weyl transform for rotationally invariant symbols

2019 ◽  
Vol 10 (4) ◽  
pp. 769-791 ◽  
Author(s):  
Norbert Ortner ◽  
Peter Wagner
Keyword(s):  
Asymptotic Behavior ◽  
Differential Operators ◽  
Symmetric Distributions ◽  
Yield Criteria ◽  
Weyl Transform ◽  
Pseudo Differential Operators ◽  
Weyl Transforms ◽  
Rotationally Invariant

Abstract Several formulas for the eigenvalues $$\lambda _j$$ λ j of the Weyl transforms $$W_\sigma $$ W σ of symbols $$\sigma $$ σ given by radially symmetric distributions are derived. These yield criteria for the boundedness and the compactness, respectively, of the pseudo-differential operators $$W_\sigma .$$ W σ . We investigate some examples by analyzing the asymptotic behavior of $$\lambda _j$$ λ j for $$j\rightarrow \infty $$ j → ∞ .

A METHOD FOR THE DIRECT INTERPRETATION OF ELECTRICAL SOUNDINGS MADE OVER A FAULT OR DIKE

Geophysics ◽  
1973 ◽  
Vol 38 (4) ◽  
pp. 762-770 ◽  
Author(s):  
Terry Lee ◽  
Ronald Green
Keyword(s):  
Bessel Functions ◽  
Direct Analysis ◽  
Hankel Transform ◽  
Approximation Technique ◽  
Polarization Data ◽  
Resistivity Data ◽  
Vertical Fault ◽  
Direct Interpretation ◽  
Electrical Soundings ◽  
Infinite Integral

The potential function for a point electrode in the vicinity of a vertical fault or dike may be expressed as an infinite integral involving Bessel functions. Beginning with such an expression, two methods are presented for the direct analysis of resistivity data measured both normal and parallel to dikes or faults. The first method is based on the asymptotic expansion of the Hankel transform of the field data and is suitable for surveys done parallel to the strike of the dike or fault. The second method is based on a successive approximation technique which starts from an initial approximate solution and iterates until a solution with prescribed accuracy is found. Both methods are suitable for programming on a digital computer and some illustrative numerical results are presented. These examples show the limitations of the methods. In addition, the application of resistivity data to the interpretation of induced‐polarization data is pointed out.

Weyl transforms for H-type groups

2014 ◽  
Vol 6 (1) ◽  
pp. 11-19 ◽  
Author(s):  
Aparajita Dasgupta ◽  
M. W. Wong
Keyword(s):  
Weyl Transforms
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