On generalized convolutions for Fourier transforms and application in solving nonlinear integral equations (Q2839823)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: On generalized convolutions for Fourier transforms and application in solving nonlinear integral equations |
scientific article; zbMATH DE number 6187731
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On generalized convolutions for Fourier transforms and application in solving nonlinear integral equations |
scientific article; zbMATH DE number 6187731 |
Statements
12 July 2013
0 references
convolution
0 references
Fourier transform
0 references
Fourier sine transform
0 references
Fourier cosine transform
0 references
Toeplitz kernel
0 references
Hankel kernel
0 references
nonlinear integral equations
0 references
system of linear integral equations
0 references
On generalized convolutions for Fourier transforms and application in solving nonlinear integral equations (English)
0 references
Using various notions \(*_i\) of convolutions (corresponding to multiplication formulas for several variants of weighted Fourier, Fourier sine, and Fourier cosine transforms), ``explicit'' formulas for solutions of systems of three linear integral equations of the types NEWLINE\[NEWLINEh+\lambda_1\varphi\mathop{*_1}f=p,NEWLINE\]NEWLINE NEWLINE\[NEWLINEf+\lambda_2\psi\mathop{*_2}g=q,NEWLINE\]NEWLINE NEWLINE\[NEWLINEg+\lambda_3\eta\mathop{*_3}h=r,NEWLINE\]NEWLINE for the unknown functions \((f,g,h)\) are obtained.
0 references
