Electronic Resource
Springer
Nonlinear differential equations and applications
3 (1996), S. 287-303
ISSN:
1420-9004
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract We give a complete answer to the problem of the finite decidability of the local extremality character of a real analytic function at a given point, a problem that found partial answers in some works by Severi and Łojasiewicz. Consider a real analytic functionf defined in a neighbourhood of a pointx 0∈R n . Restrictf to the spherical surface centered inx 0 and with radiusr≥0 and take its infimumm(r) and its supremumM(r). We establish some properties ofm(r) andM(r) for smallr〉0. In particular, we prove that they have asymptotic expansions of the formf(x 0)+c·(r α+o(r α)) asr→0 for a realc and a rational α≥1 (of course the parameters will usually be different form andM).
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01194068
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