Vol. 66, No. 1, 1976

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Norms of powers of absolutely convergent Fourier series: an example

Charles Henry Heiberg

Vol. 66 (1976), No. 1, 131–152
Abstract

Let f be defined on T2 and have an absolutely convergent Fourier series

             ∑
f(eiσ1,eiσ2) =    fmeim1 σ1eim2σ2.

Set f= |fm| and f22 = |fm|2. In this paper the asymptotic behavior of fk, as k →∞, is studied.

Mathematical Subject Classification
Primary: 42A92, 42A92
Milestones
Received: 14 February 1975
Published: 1 September 1976
Authors
Charles Henry Heiberg