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On the Asymptotic Expansion of Hadamard Products

✍ Scribed by Andreas Sauer

Publisher
John Wiley and Sons
Year
2009
Tongue
English
Weight
304 KB
Volume
186
Category
Article
ISSN
0025-584X

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✦ Synopsis

We consider functions f and g which are holomoxphic on closed sectors in 4: where they admit an asymptotic representation at 00 in the form of power series in z-' . We give a simple geometrical condition under which the Hadamard product f * g of f and g porsemes again an ~y m p totic expansion at 00. It turns out that the asymptotic expansion of f t g is essentially the formal H s d a m d product of the asymptotic expansions of f and g . Our result yields a sli& generaliestion of a well known theoran of W. B. m.

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