An integral transform of generalized functions. II

1997 ◽  
Vol 23 (1) ◽  
pp. 115-126
Author(s):  
Anil Kumar Mahato ◽  
Анил Кумар махато
Keyword(s):  
Integral Transform ◽  
Generalized Functions

A Mixed Parseval's Equation And a Generalized Hankel Transformation of Distributions

1989 ◽  
Vol 41 (2) ◽  
pp. 274-284 ◽  
Author(s):  
J. J. Betancor
Keyword(s):  
Dual Space ◽  
Integral Transform ◽  
Generalized Functions ◽  
Generalized Function ◽  
Hankel Transformation ◽  
Formula One ◽  
Image Position ◽  
Complex Valued

Let an integral transform T﹛f﹜ of a complex valued function f(x) defined over the interval (0, ∞) be defined as One of the most usual procedures to extend the classical transform (l.a) to generalized functions consists in constructing a space A of testing functions over (0, ∞) which is closed with respect to the classical transform (l.a) and then the corresponding transform of the generalized function/ of the dual space of A is defined through This approach has been followed by L. Schwartz [13] and A. H. Zemanian [20], amongst others.

scholarly journals Some extensions of a certain integral transform to a quotient space of generalized functions

2015 ◽  
Vol 13 (1) ◽  
Author(s):  
Shrideh K.Q. Al-Omari ◽  
Jafar F. Al-Omari
Keyword(s):  
Quotient Space ◽  
Integral Transform ◽  
Generalized Functions ◽  
Space Of Generalized Functions

AbstractIn this paper, we establish certain spaces of generalized functions for a class of ɛ

scholarly journals A New Representation of the Generalized Krätzel Function

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2009
Author(s):  
Asifa Tassaddiq
Keyword(s):  
Fourier Transform ◽  
Integral Transform ◽  
Integral Transforms ◽  
Delta Function ◽  
Generalized Functions ◽  
Natural Consequence ◽  
Test Functions ◽  
Definition Of ◽  
The Relationship ◽  
Krätzel Integral

The confluence of distributions (generalized functions) with integral transforms has become a remarkably powerful tool to address important unsolved problems. The purpose of the present study is to investigate a distributional representation of the generalized Krätzel function. Hence, a new definition of these functions is formulated over a particular set of test functions. This is validated using the classical Fourier transform. The results lead to a novel extension of Krätzel functions by introducing distributions in terms of the delta function. A new version of the generalized Krätzel integral transform emerges as a natural consequence of this research. The relationship between the Krätzel function and the H-function is also explored to study new identities.

CONVERGENCE ACCELERATION OF INTEGRAL TRANSFORM SOLUTIONS

2001 ◽  
Vol 3 (1) ◽  
pp. 6
Author(s):  
Mikhail D. Mikhailov ◽  
Renato M. Cotta
Keyword(s):  
Integral Transform ◽  
Convergence Acceleration
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