On Volterra partial integral equations in the space of continuous functions of three variables |
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Authors: | E V Frolova |
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Institution: | (1) Lipetsk State Pedagogical University, Lipetsk, Russia |
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Abstract: | It is well known that any Volterra integral equation of the second kind with compact operator is uniquely solvable. Partial
integral operators are not compact, even in the general case of continuous kernels. Unique solvability conditions for Volterra
partial integral equations of the second kind in the space of continuous functions of three variables are considered. Conditions
for a Volterra partial integral equation to be equivalent to a three-dimensional Volterra integral equation with compact operator
are obtained. Continuum analogues of matrix equations for some problems of scattering theory are reduced to the Volterra partial
integral equations under examination.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 38, Suzdal
Conference-2004, Part 3, 2006. |
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Keywords: | |
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