On the Non-Equivalence of Rearranged Walsh and Trigonometric Systems in L_p

2003/08/10 by Aicke Hinrichs, Jörg Wenzel, Hinrichs, Aicke +1
Mathematics · #42C20 (primary) 42C10 #46B15 (secondary) #Analytic Number Theory Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical Dynamics and Fractals #Mathematics and Applications #math.FA #msc:42C10 #msc:42C20 #msc:46B15

paper · pdf · doi:10.48550/arxiv.math/0308091

18 pages, to be published in Stud. Math

arxiv created 2003/08/10 · openalex publication_date 2003/08/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the question whether the trigonometric system can be equivalent to some rearrangement of the Walsh system in L_p for some p<>2. We show that this question is closely related to a combinatorial problem. This enables us to prove non-equivalence for a number of rearrangements. Previously this was known for the Walsh-Paley order only.

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