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Solvability of convolution equation in the Gevrey class of functions analytic in a nonconvex region

O. V. Gorina

Rostov State University

Abstract: In the Gevrey space $A(q)$ of functions analytic in a nonconvex bounded region in $\mathbf{C}^-$, we consider $a$ convolution operator $L$ generated by some entire functiona. A necessary and sufficient condition under which the equality $L(A(q))=A(q)$ holds is established.

UDC: 517

Received: 16.05.1990

 English version: Mathematical Notes, 1992, 52:3, 895–902

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