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Algebra i Analiz, 2022, Volume 34, Issue 3, Pages 51–92 (Mi aa1809)  
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Stationary phase method, powers of functions, and applications to functional analysis

H. Quefféleca, R. Zaroufbc

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
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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.
Funding agency Grant number
Agence Nationale de la Recherche ANR-11-LABX-0007-01
18-CE40-0035
The first author acknowledges support from the Labex CEMPI (ANR-11-LABX-0007-01). The second author acknowledges support from the project ANR 18-CE40-0035.
Received: 14.10.2021
English version:
St. Petersburg Mathematical Journal, 2023, Volume 34, Issue 3, Pages 347–377
DOI: https://doi.org/10.1090/spmj/1757
Document Type: Article
Language: English
Citation: H. Queffélec, R. Zarouf, “Stationary phase method, powers of functions, and applications to functional analysis”, Algebra i Analiz, 34:3 (2022), 51–92; St. Petersburg Math. J., 34:3 (2023), 347–377
Citation in format AMSBIB
\Bibitem{QueZar22}
\by H.~Queff\'elec, R.~Zarouf
\paper Stationary phase method, powers of functions, and applications to functional analysis
\jour Algebra i Analiz
\yr 2022
\vol 34
\issue 3
\pages 51--92
\mathnet{http://mi.mathnet.ru/aa1809}
\transl
\jour St. Petersburg Math. J.
\yr 2023
\vol 34
\issue 3
\pages 347--377
\crossref{https://doi.org/10.1090/spmj/1757}
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