Key moments of the mutual influence of the Polish and Soviet schools of nonlinear functional analysis in the 1920s--1950s

Egor Mikhailovich Bogatov

Antiquitates Mathematicae, Tome 11 (2017), pp. 131 - 156.

Résumé

The paper includes key aspects of the history of development of qualitative methods of non-linear functional analysis (fixed point theorems, theory of mapping degree, theory of Orlicz spaces), within the framework of which Polish-Soviet interaction was most clearly manifested. In the period up to the mid-twentieth century these areas were advanced by the representatives of Lvov Mathematical School, Warsaw Mathematical School, Moscow Mathematical School and Odessa Mathematical School. Examination of their results is a significant part of this work. Much attention is paid to the investigations of the Soviet mathematician M.A. Krasnosel'skii, who used the achievements of J. Schauder and K. Borsuk as well as Orlicz spaces for solving a wide class of problems in qualitative theory of nonlinear integral equations.

Détail

DOI : 10.14708/am.v11i0.5124

Classification : 01A60, 01A72, 46-03
Mots-clés : Polish school of functional analysis, Soviet school of functional analysis, fixed point theorem, Orlicz space, nonlinear integral equations, mapping degree, convex sets, retracts theory

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