By Michael B. Marcus
In this e-book the authors provide the 1st valuable and enough stipulations for the uniform convergence a.s. of random Fourier sequence on in the neighborhood compact Abelian teams and on compact non-Abelian teams. in addition they receive many similar effects. for instance, at any time when a random Fourier sequence converges uniformly a.s. it additionally satisfies the crucial restrict theorem. The equipment built are used to check a few questions in harmonic research that aren't intrinsically random. for instance, a brand new characterization of Sidon units is derived.
The significant effects rely seriously at the Dudley-Fernique worthwhile and adequate for the continuity of desk bound Gaussian tactics and on contemporary paintings on sums of autonomous Banach house valued random variables. it really is noteworthy that the proofs for the Abelian case instantly expand to the non-Abelian case as soon as the right kind definition of random Fourier sequence is made. In doing this the authors receive new effects on sums of autonomous random matrices with components in a Banach area. the ultimate bankruptcy of the ebook indicates a number of instructions for extra research.
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