Functiones et Approximatio Commentarii Mathematici

The Bohnenblust-Hille cycle of ideas from a modern point of view

Andreas Defant and Pablo Sevilla-Peris

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In 1931 H.F. Bohnenblust and E. Hille published a very important paper in which not only did they solve a long standing problem on convergence of Dirichlet series, but also gave a~general version of a celebrated inequality of Littlewood. Although it is full of extremely valuable mathematical ideas, the paper has been overlooked for a~long time and even today we feel that it does not get the credit it deserves. This may be caused by the not always accessible style that makes that the ideas are sometimes hidden. It is our intention to try to study the paper from a~modern point of view and to bring to light the valuable aspects we believe it has.

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Funct. Approx. Comment. Math., Volume 50, Number 1 (2014), 55-127.

First available in Project Euclid: 27 March 2014

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Primary: 30B50: Dirichlet series and other series expansions, exponential series [See also 11M41, 42-XX]
Secondary: 46G25: (Spaces of) multilinear mappings, polynomials [See also 46E50, 46G20, 47H60] 46E50: Spaces of differentiable or holomorphic functions on infinite- dimensional spaces [See also 46G20, 46G25, 47H60]

Dirichlet series Bohnenblust-Hille inequality polynomials Bohr's problem


Defant, Andreas; Sevilla-Peris, Pablo. The Bohnenblust-Hille cycle of ideas from a modern point of view. Funct. Approx. Comment. Math. 50 (2014), no. 1, 55--127. doi:10.7169/facm/2014.50.1.2.

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