期刊
JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS
卷 16, 期 5, 页码 676-692出版社
BIRKHAUSER BOSTON INC
DOI: 10.1007/s00041-009-9112-y
关键词
Dirichlet series; Abscissa of convergence; Bounded analytic function; Random variable; Dirichlet polynomial; Walsh matrix; Rudin-Shapiro type sequence; Prime number
We consider here the algebra of functions which are analytic and bounded in the right half-plane and can moreover be expanded as an ordinary Dirichlet series. We first give a new proof of a theorem of Bohr saying that this expansion converges uniformly in each smaller half-plane; then, as a consequence of the alternative definition of this algebra as an algebra of functions analytic in the infinite-dimensional polydisk, we first observe that it does not verify the corona theorem of Carleson; and then, we give in a deterministic way a new quantitative proof of the Bohnenblust-Hille optimality theorem, through the construction of a generalized Rudin-Shapiro sequence of polynomials. Finally, we compare this proof with probabilistic ones.
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