An abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniqueness

Department of Mathematics2024-11-0920100022-123610.1016/j.jfa.2009.09.0212-s2.0-70350596213http://dx.doi.org/10.1016/j.jfa.2009.09.021https://hdl.handle.net/20.500.14288/7927Let E be a compact perfect subset of the real line R such that the restriction of the Fourier transform a bar right arrow (a) over cap vertical bar(E) from L(1)(R) into C(E) is onto. Helson proved that then, for mu is an element of M(E), lim(vertical bar y vertical bar ->infinity vertical bar) (u) over cap (y)vertical bar = 0 is possible only if mu = 0. In this paper we present an abstract version of this theorem of Helson and provide some applications of it to the study of sets of spectral synthesis and sets of uniqueness.MathematicsAn abstract form of a theorem of Helson and applications to sets of synthesis and sets of uniquenessJournal Article272112900011Q18784