scholarly journals Paley-Wiener-Type Theorem for a Class of Integral Transforms Arising from a Singular Dirac System

2000 ◽  
Vol 19 (3) ◽  
pp. 695-712 ◽  
Author(s):  
A.I. Zayed ◽  
Vu Kim Tuan
Keyword(s):  
Type Theorem ◽  
Integral Transforms ◽  
Dirac System ◽  
Wiener Type

scholarly journals Some results of Watson, Plancherel type integral transforms related to the Hartley, Fourier convolutions and applications

2021 ◽  
Author(s):  
Tuan Trinh
Keyword(s):  
Differential Equations ◽  
Type Theorem ◽  
Sufficient Conditions ◽  
Integral Transforms ◽  
System Of Differential Equations ◽  
Symmetric Form ◽  
Original Function ◽  
Type Integral ◽  
Necessary And Sufficient ◽  
Sequence Of Functions

In this work, we study the Watson-type integral transforms for the convolutions related to the Hartley and Fourier transformations. We establish necessary and sufficient conditions for these operators to be unitary in the L 2 (R) space and get their inverse represented in the conjugate symmetric form. Furthermore, we also formulated the Plancherel-type theorem for the aforementioned operators and prove a sequence of functions that converge to the original function in the defined L 2 (R) norm. Next, we study the boundedness of the operators (T k ). Besides, showing the obtained results, we demonstrate how to use it to solve the class of integro-differential equations of Barbashin type, the differential equations, and the system of differential equations. And there are numerical examples given to illustrate these.

scholarly journals Huygens’ principle and a Paley–Wiener type theorem on Damek–Ricci spaces

2010 ◽  
Vol 17 (2) ◽  
pp. 327-340 ◽  
Author(s):  
Francesca Astengo ◽  
Bianca Di Blasio
Keyword(s):  
Type Theorem ◽  
Wiener Type ◽  
Huygens Principle

scholarly journals Paley-Wiener-type theorem for polynomial ultradifferentiable functions

2015 ◽  
Vol 7 (2) ◽  
pp. 271-279
Author(s):  
S.V. Sharyn
Keyword(s):  
Laplace Transformation ◽  
Type Theorem ◽  
Ultradifferentiable Functions ◽  
Wiener Theorem ◽  
Wiener Type

The image of the space of ultradifferentiable functions with compact supports under Fourier-Laplace transformation is described. An analogue of Paley-Wiener theorem for polynomial ultradifferentiable functions is proved.

scholarly journals A Wiener type theorem for (U(p,q) ,Hn)

2010 ◽  
Vol 119 (2) ◽  
pp. 169-180
Author(s):  
Linda Saal
Keyword(s):  
Type Theorem ◽  
Wiener Type
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