Vol. 55, No. 2, 1974

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Linear Pincherle sequences

Ed Dubinsky

Vol. 55 (1974), No. 2, 361–369

Dragilev’s theory of regular bases in nuclear Fréchet spaces is applied to obtain necessary and sufficient conditions in terms of the zeros for a linear Pincherle sequence to be a basis for the space R of functions analytic on the interior of the disk of radius R . It is shown that a linear Pincherle basis is always proper. All possible phenomena for the basis radius of a linear Pincherle sequence are exhibited. In this connection it is shown that for any finite R0 > 0 there is a sequence of analytic functions which is a basis for R if and only if R R0 or R = .

Mathematical Subject Classification 2000
Primary: 46E10
Received: 6 July 1973
Published: 1 December 1974
Ed Dubinsky