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- On functions uniquely determined by their asymptotic expansion
- Gillam, D. W. H.; Gurarii, V. P.
- We present a maximal class of analytic functions. The elements of this class are uniquely determined by their asymptotic expansions. We also discuss the possibility of recovery of a function from the coefficients of its asymptotic series. In particular, we consider the problem of recovering by using Borel summation. The last published result in this direction was obtained by Alan Sokal in 1980, but his paper well known to physicists (in quantum field theory) seems to have remained unnoticed by mathematicians.
- Publication type
- Journal article
- Research centre
- Swinburne University of Technology. Faculty of Engineering and Industrial Sciences
- Functional Analysis and its Applications, Vol. 40, no. 4 (2006), pp. 273-284
- Publication year
- Differential equations in complex domain; Gevrey expansions; Laplace transforms in complex domain; Watson's uniqueness theorem
- Publisher URL
- Copyright © Springer Science+Business Media, Inc. 2006. Accepted manuscript of the paper reproduced here in accordance with the copyright policy of the publisher. The original publication is available at www.springerlink.com.
- Full text
- Peer reviewed