This article is cited in 22 papers

A generalization of the Wiener–Hopf method for convolution equations on a finite interval with symbols having power-like asymptotics at infinity

B. V. Pal'tsev


Abstract: A generalization of the Wiener–Hopf method is obtained for convolution equations on the finite interval $(-T,T)$
$$ (\mathbf Ku)(t)=f(t),\qquad|t|<T, $$
where $\mathbf K$ is the convolution operator $\mathbf Ku(t)=(r_{(-T,T)}k*u)(t)$, $u(t)\in\mathscr S'(\mathbf R^1)$, $u(t)\equiv0$ for $|t|>T$, $*$ is the convolution operation, $k=k(t)$ is a kernel belonging to $\mathscr S'(\mathbf R^1)$, $r_{(-T,T)}$ is the operator of restriction of a generalized function to the interval $(-T,T)$, and $f(t)\in\mathscr D'(-T,T)$. Here $\mathscr S(\mathbf R^1)$ and $\mathscr S'(\mathbf R^1)$ are the Schwartz spaces of rapidly decreasing test functions and generalized functions of slow growth on $\mathbf R^1$, respectively.
Bibliogrpahy: 19 titles.

UDC: 517.948

MSC: Primary 30E25, 45E10; Secondary 46F12, 47A53

Received: 19.05.1980

 English version: Mathematics of the USSR-Sbornik, 1982, 41:3, 289–328

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