Vol. 28, No. 1, 1969

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Gap series and an example to Malliavin’s theorem

Robert P. Kaufman

Vol. 28 (1969), No. 1, 117–119
Abstract

O. Malliavin’s celebrated theorem of spectral nonsynthesis is based on a real function f of class A

f(t) = n=1a n cosnt + n=1b n sinnt,
|an| + |bn| < ,
for which −∞|u|∥eiufdu < .

Here and in general g supn|ĝ(n)|. This note presents a method for constructing a function f, based on a gap property and a method of estimation of Kahane.

Mathematical Subject Classification
Primary: 42.58
Milestones
Received: 9 October 1967
Published: 1 January 1969
Authors
Robert P. Kaufman