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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2009, Number 4, Pages 39–42
(Mi ivm1318)
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This article is cited in 2 scientific papers (total in 2 papers)
Regularization of a three-element functional equation
S. A. Modina Kazan State Power Engineering University
Abstract:
In this paper we study the three-element functional equation
$$
(V\Phi)(z)\equiv\Phi(iz)+\Phi(-iz)+G(z)\Phi\biggl(\frac1z\biggr)=g(z),\qquad z\in R,
$$
subject to
$$
R\colon\ |z|<1,\quad|\arg z|<\frac\pi4.
$$
We assume that the coefficients $G(z)$ and $g(z)$ are holomorphic in $R$ and their boundary values $G^+(t)$ and $g^+(t)$ belong to $H(\Gamma)$, $G(t)G(t^{-1})=1$. We seek for solutions $\Phi(z)$ in the class of functions holomorphic outside of $\overline R$ such that they vanish at infinity and their boundary values
$\Phi^-(t)$ also belong to $H(\Gamma)$.
Using the method of equivalent regularization, we reduce the problem to the 2nd kind integral Fredholm equation.
Keywords:
functional equation, holomorphic function, regularization method, rotation group of a dihedron.
Received: 18.01.2007
Citation:
S. A. Modina, “Regularization of a three-element functional equation”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 4, 39–42; Russian Math. (Iz. VUZ), 53:4 (2009), 31–33
Linking options:
https://www.mathnet.ru/eng/ivm1318 https://www.mathnet.ru/eng/ivm/y2009/i4/p39
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Abstract page: | 264 | Full-text PDF : | 37 | References: | 28 | First page: | 4 |
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