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2010•Moscow University Mathematics BulletinRequires access

Connection between sets of uniqueness for multiplicative systems of functions and sets of uniqueness for multiplicative transforms

T. A. Zhereb’eva

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Abstract

A problem of uniqueness for series over multiplicative systems of functions and for multiplicative transforms is considered. It is shown that each set of uniqueness for a multiplicative transform is specified by a countable collection of sets of uniqueness for series over the corresponding multiplicative system of functions. Each set of uniqueness for a series over a multiplicative system of functions is a portion on [0, 1) of some set of uniqueness for the corresponding multiplicative transform.

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What this paper is about

A problem of uniqueness for series over multiplicative systems of functions and for multiplicative transforms is considered. It is shown that each set of uniqueness for a multiplicative transform is specified by a countable collection of sets of uniqueness for series over the corresponding multiplicative system of functions. Each set of uniqueness for a series over a multiplicative system of functions is a portion on [0, 1) of some set of uniqueness for the corresponding multiplicative transform.

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Available abstract

A problem of uniqueness for series over multiplicative systems of functions and for multiplicative transforms is considered. It is shown that each set of uniqueness for a multiplicative transform is specified by a countable collection of sets of uniqueness for series over the corresponding multiplicative system of functions. Each set of uniqueness for a series over a multiplicative system of functions is a portion on [0, 1) of some set of uniqueness for the corresponding multiplicative transform.

Key concepts: Uniqueness, Multiplicative function, Mathematics, Countable set, Set (abstract data type), Pure mathematics, Mathematical analysis, Computer science

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