This article is cited in 9 papers

Distribution of the zeros of canonical products and weighted condensation index

V. B. Sherstyukov

National Engineering Physics Institute "MEPhI", Moscow

Abstract: Canonical products with symmetrically positioned real zeros are considered. The question of the measurability of the sequence of zeros in terms of the weighted condensation index is treated. A natural class of weight functions, for which a finite condensation index ensures that the sequence of zeros is measurable, is distinguished. The main condition characterizing this class is shown to be sharp.
Bibliography: 31 titles.

Keywords: canonical product, measurable sequence of zeros, condensation index.

UDC: 517.547.2

MSC: Primary 30D15; Secondary 26A12

Received: 11.11.2014 and 19.01.2015

DOI: 10.4213/sm8446

 English version: Sbornik: Mathematics, 2015, 206:9, 1299–1339

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