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Cauchy problem for evolution equations with an infinite-order differential operator: II

Cauchy problem for evolution equations with an infinite-order differential operator: II ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 9, pp. 1181–1193.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c V.V. Gorodetskii, R.S. Kolisnyk, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 9, pp. 1155–1167. PARTIAL DIFFERENTIAL EQUATIONS Cauchy Problem for Evolution Equations with an Infinite-Order Differential Operator: II V. V. Gorodetskii and R. S. Kolisnyk Chernovtsy National University, Chernovtsy, Ukraine Received April 3, 2006 DOI: 10.1134/S0012266107090017 The present paper is a continuation of [1], where we constructed function spaces of the type C, which consist of entire functions decreasing more rapidly than exp{−|x|}, x ∈ R, on the real axis β β as |x|→ ∞; known spaces of the type S (S , S ,and S , {α, β}⊂ (0, 1)) constructed by Gelfand α α and Shilov, as well as spaces of the type W constructed by Gurevich, form subspaces of the above- mentioned spaces. We studied the topological structure of such spaces, analyzed properties of basic operations in these spaces, characterized spaces of the type C via the behavior of functions in these spaces and their derivatives on the real axis, proved theorems on the Fourier transform of spaces of the type C http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Cauchy problem for evolution equations with an infinite-order differential operator: II

Gorodetskii, V. V.; Kolisnyk, R. S.
Differential Equations , Volume 43 (9) – Sep 1, 2007
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Publisher
Springer Journals
Copyright
Copyright © Pleiades Publishing, Ltd. 2007
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1134/s0012266107090017
Publisher site
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Abstract

ISSN 0012-2661, Differential Equations, 2007, Vol. 43, No. 9, pp. 1181–1193.  c Pleiades Publishing, Ltd., 2007. Original Russian Text  c V.V. Gorodetskii, R.S. Kolisnyk, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 9, pp. 1155–1167. PARTIAL DIFFERENTIAL EQUATIONS Cauchy Problem for Evolution Equations with an Infinite-Order Differential Operator: II V. V. Gorodetskii and R. S. Kolisnyk Chernovtsy National University, Chernovtsy, Ukraine Received April 3, 2006 DOI: 10.1134/S0012266107090017 The present paper is a continuation of [1], where we constructed function spaces of the type C, which consist of entire functions decreasing more rapidly than exp{−|x|}, x ∈ R, on the real axis β β as |x|→ ∞; known spaces of the type S (S , S ,and S , {α, β}⊂ (0, 1)) constructed by Gelfand α α and Shilov, as well as spaces of the type W constructed by Gurevich, form subspaces of the above- mentioned spaces. We studied the topological structure of such spaces, analyzed properties of basic operations in these spaces, characterized spaces of the type C via the behavior of functions in these spaces and their derivatives on the real axis, proved theorems on the Fourier transform of spaces of the type C

Journal

Differential Equations – Springer Journals

Published: Sep 1, 2007

Keywords: Cauchy Problem; Evolution Equation; Entire Function; Real Axis; Analytic Continuation

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