H. Queffélec, R. Zarouf, “Stationary phase method, powers of functions, and applications to functional analysis”, Algebra i Analiz, 2022, Volume 34, Issue 3,Pages <nobr>51

Expository Surveys

Stationary phase method, powers of functions, and applications to functional analysis

H. Queffélec^a, R. Zarouf^bc

^a Université Lille Nord de France, USTL, Laboratoire Paul Painlevé, U.M.R. CNRS 8524 et Fédération, CNRS Nord-Pas-de-Calais, FR 2956 F-59 655, Villeneuve d' Ascq Cedex, France
^b Aix-Marseille Université, Laboratoire Apprentissage, Didactique, Evaluation, Formation, 32 Rue Eugène Cas CS 90279 13248, Marseille Cedex 04, France
^c Department of Mathematics and Mechanics, St.Petersburg State University, 28, Universitetski pr., St. Petersburg, 198504, Russia

Abstract: The utility of the (weighted) van der Corput inequalities or of the stationary phase method is illustrated with various examples borrowed from: differentiability issues (Riemann's function and related); functional analysis on Banach spaces or algebras of analytic functions (composition operators); and local Banach space geometry (Schäffer's problem).

Keywords: stationary phase method, powers of functions, Blaschke factors, Wiener space, Dirichlet series, composition operators, Schäffer's problem, Toeplitz operators.

Received: 14.10.2021

Language: English