Rearrangements and category

Russell Gene Bilyeu, Robert Richard Kallman and Paul Weldon Lewis

Vol. 121 (1986), No. 1, 41–46

DOI: 10.2140/pjm.1986.121.41

Abstract

Kolmogorov stated, and Zahorski proved, that there exists an L²- Fourier series such that some rearrangement of it diverges almost everywhere. Kac and Zygmund asked if the set of rearrangements which make this Fourier series diverge almost everywhere is first category or second category. A general theorem is proved which has as a special case that the set of rearrangements in question is residual.

Mathematical Subject Classification 2000

Primary: 42A20

Secondary: 54H20

Milestones

Received: 10 May 1984

Published: 1 January 1986