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# On holomorphic solutions of the heat equation with a Volterra operator coefficient

### Abstract

Let $A$ be a bounded operator on a Hilbert space and $g$ a vector-valued function, which is holomorphic in a neighborhood of zero. The question about existence of holomorphic solutions of the Cauchy problem $\left\{ \begin{array}{ll} \displaystyle\frac{\partial u}{\partial t}= A\displaystyle\frac{\partial^{2}u}{\partial x^2}\\ u(0,x)=g(x) \\ \end{array} \right.$ is considered in the paper.

### Article Information

 Title On holomorphic solutions of the heat equation with a Volterra operator coefficient Source Methods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 329-332 MathSciNet MR2374834 Copyright The Author(s) 2007 (CC BY-SA)

### Authors Information

Sergey Gefter
School of Mechanics and Mathematics, Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine

### Citation Example

Sergey Gefter and Anna Vershynina, On holomorphic solutions of the heat equation with a Volterra operator coefficient, Methods Funct. Anal. Topology 13 (2007), no. 4, 329-332.

### BibTex

@article {MFAT411,
AUTHOR = {Gefter, Sergey and Vershynina, Anna},
TITLE = {On holomorphic solutions of the heat equation with a Volterra operator coefficient},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {4},
PAGES = {329-332},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=411},
}