On a problem of Kahane in higher dimensions

2016/11/16 by James Wright, Wright, James
Mathematics · #42B05 #42B08 #42B20 #Advanced Harmonic Analysis Research #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Analysis and Transform Methods

paper · pdf · doi:10.48550/arxiv.1611.05398

openalex publication_date 2016/11/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We characterise those real analytic mappings between any pair of tori which carry absolutely convergent Fourier series to uniformly convergent Fourier series via composition. We do this with respect to rectangular summation. We also investigate uniform convergence with respect to square sums and highlight the differences which arise.

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