caa a22 4500 477091504 CHVBK 20180405111516.0 cr unu---uuuuu 170330e19960901xx s 000 0 eng 10.1007/BF01194068 doi (NATIONALLICENCE)springer-10.1007/BF01194068 Local extrema of analytic functions [Elektronische Daten] [Angelo Barone-Netto, Gianluca Gorni, Gaetano Zampieri] 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). Birkhäuser Verlag, 1996 Barone-Netto Angelo Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66 281, 05389-970, São Paulo, SP, Brazil aut Gorni Gianluca Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 208, 33100, Udine, Italy aut Zampieri Gaetano Dipartimento di Matematica, Università di Messina, Salita Sperone 31, 98166, Sant'Agata, Messina, Italy aut Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/3(1996-09-01), 287-303 1021-9722 3:3<287 1996 3 30 https://doi.org/10.1007/BF01194068 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF01194068 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Barone-Netto Angelo Instituto de Matemática e Estatística, Universidade de São Paulo, Caixa Postal 66 281, 05389-970, São Paulo, SP, Brazil aut NATIONALLICENCE 700 1- Gorni Gianluca Dipartimento di Matematica e Informatica, Università di Udine, via delle Scienze 208, 33100, Udine, Italy aut NATIONALLICENCE 700 1- Zampieri Gaetano Dipartimento di Matematica, Università di Messina, Salita Sperone 31, 98166, Sant'Agata, Messina, Italy aut NATIONALLICENCE 773 0- Nonlinear Differential Equations and Applications NoDEA Birkhäuser-Verlag 3/3(1996-09-01), 287-303 1021-9722 3:3<287 1996 3 30 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer