Local extrema of analytic functions
| Autor: | Gianluca Gorni, Angelo Barone-Netto, Gaetano Zampieri |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 1996 |
| Předmět: | |
| Zdroj: | Repositório Institucional da USP (Biblioteca Digital da Produção Intelectual) Universidade de São Paulo (USP) instacron:USP |
| Popis: | 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). |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|