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Zeros of successive
iterates of multiplier-sequence operators
Carl L. Prather and Ken Shaw |
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Vol. 104 (1983), No. 1, 205–218
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Abstract |
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The authors study the zero free regions of iterates of multiplier-sequence operators for (i) functions analytic in the disc |z| < R and (ii) functions analytic in |z| > T. Integral representations for the iterates of each class of functions are given. As a consequence the authors give a generalization of the Post-Widder inversion formula. Other applications include an investigation of the zero free regions for iterates of fractional integrals as well as connections between results obtained here and recent final set results for iterates of operators on balanced sums. |
Mathematical Subject Classification 2000
Primary: 30C99
Secondary: 30D99, 44A15
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Milestones
Received: 2 June 1980
Published: 1 January 1983
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Authors |
| Carl L. Prather | |
| Ken Shaw | |
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