Published April 1975
| public
Journal Article
On an infinite series of Abel occurring in the theory of interpolation
- Creators
- Luxemburg, W. A. J.
Abstract
The purpose of this paper is to show that for a certain class of functions f which are analytic in the complex plane possibly minus (−∞, −1], the Abel series ! is convergent for all β>0. Its sum is an entire function of exponential type and can be evaluated in terms of f. Furthermore, it is shown that the Abel series of f for small β>0 approximates f uniformly in half-planes of the form Re(z) ⩾ − 1 + δ, δ>0. At the end of the paper some special cases are discussed.
Additional Information
© 1975 Published by Elsevier Inc. Under an Elsevier user license. Communicated by P. L. Butzer. Dedicated to Professor G. G. Lorentz on the occasion of his sixty-fifth birthday. Work on this paper was supported in part by NSF Grant 23392.Additional details
- Eprint ID
- 90201
- Resolver ID
- CaltechAUTHORS:20181009-135412183
- GP-23392
- NSF
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2018-10-10Created from EPrint's datestamp field
- Updated
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2021-11-16Created from EPrint's last_modified field