Trigonometric sums associated with pseudo-measures
Fourier Analysis of Riemann Distributions and Explicit Formulas.
(LF) Spaces and Distributions on Compact Groups and Spectral Synthesis on R-2...Z.
Analytic Representation of Generalized Functions.
Support Preserving Measure Algebras and Spectral Synthesis.
A Support Preserving Hahn-Banach Property to Determine Helson-S Sets.
Zeta functions for idelic pseudo-measures
Idele characters in spectral synthesis on
Let , . We construct Dirichlet series where for each fixed in a half plane, , as a function of , is a non-synthesizable absolutely convergent Fourier series. Because of the way the frequencies in are chosen, we are motivated to introduce a class of synthesizable absolutely convergent Fourier series which are defined in terms of idele characters. We solve the “problem of analytic continuation” in this setting by constructing pseudo-measures, determined by idele characters, when .
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