Toeplitz plus Hankel integral equation. (English) Zbl 1235.44011
The integral equation with the Toeplitz plus Hankel kernel is of the form
\[
f(x)+ \int^\infty_0 [k_1(x+ y)+ k_2(x- y)] f(y)\,dy= g(x),\quad x> 0,
\]
here \(g\), \(k_1\), \(k_2\) are given and \(f\) is a unknown function. The solution of equation in closed form in the general case is still open.
In this paper the authors consider several new special cases of this equation with the help of generalized convolution.
In this paper the authors consider several new special cases of this equation with the help of generalized convolution.
Reviewer: Alexandr L. Brodskij (Severodonetsk)
MSC:
| 44A35 | Convolution as an integral transform |
| 45E10 | Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
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