Functional Analysis and Its Applications

, Volume 52, Issue 1, pp 35–44 | Cite as

Summation of Unordered Arrays

  • E. V. Shchepin


An approach to the summation of unordered number and matrix arrays based on ordering them by absolute value (greedy summation) is proposed. Theorems on products of greedy sums are proved. A relationship between the theory of greedy summation and the theory of generalized Dirichlet series is revealed. The notion of asymptotic Dirichlet series is considered.

Key words

greedy sum unordered sum theorem on multiplications of sums generalized Dirichlet series asymptotic Dirichlet series Riesz means generic zeta-function 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Steklov Mathematical Institute of Russian Academy of SciencesMoscowRussia

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