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On Spectral Synthesis for One Point

Published online by Cambridge University Press:  20 November 2018

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In [2, page 3831], Varopoulos proves that for any ∈ > 0 there exists a function on a neighbourhood of 0. Indeed, if 0 < ∈ < π/2, then f(x) defined to be equal to 1 - e when -eix, linear on [∈, 2π - ∈] and of period 2π, is an example of such a function.

The above result can be used to give a direct proof of the following result without reference to the L2 theory [1, Theorem 2.6.4].

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1969

References

1. Rudin, W., Fourier analysis on groups. (Interscience, 1962).Google Scholar
2. Varopoulos, N. Th., Sur les ensembles parfaits et les séries trigonométriques. C.R. Acad. Se. Paris 260 (1965) 46684670, 5165–5168, 5997–6000.Google Scholar