BESSEL TYPE INTEGRAL TRANSFORMS ON THE SPACE Lv,r

2004 ◽  
Keyword(s):  
Integral Transforms ◽  
Type Integral

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 H-function with complex parameters I: existence

2001 ◽  
Vol 25 (9) ◽  
pp. 571-586
Author(s):  
Fadhel A. Al-Musallam ◽  
Vu Kim Tuan
Keyword(s):  
Sufficient Conditions ◽  
Integral Transforms ◽  
Necessary And Sufficient Conditions ◽  
Special Cases ◽  
Type Integral ◽  
Necessary And Sufficient

AnH-function with complex parameters is defined by a Mellin-Barnes type integral. Necessary and sufficient conditions under which the integral defining theH-function converges absolutely are established. Some properties, special cases, and an application to integral transforms are given.

Sign in / Sign up

Export Citation Format

Share Document