Affine Bessel sequences and Nikishin’s example | Zendy

В. А. Миронов | Zendy; Abdizhahan Sarsenbi | Zendy; П. А. Терехин | Zendy

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Affine Bessel sequences and Nikishin’s example

Author(s) -

В. А. Миронов,

Abdizhahan Sarsenbi,

П. А. Терехин

Publication year - 2017

Publication title -

filomat

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.449

H-Index - 34

eISSN - 2406-0933

pISSN - 0354-5180

DOI - 10.2298/fil1704963m

Subject(s) - mathematics , bessel function , affine transformation , pure mathematics , connection (principal bundle) , hilbert space , measure (data warehouse) , affine combination , affine plane (incidence geometry) , mathematical analysis , geometry , computer science , plane curve , database

We study affine Bessel sequences in connection with the spectral theory and the multishift structure in Hilbert space. We construct a non-Besselian affine system fun(x)g1 n=0 generated by continuous periodic function u(x). The result is based on Nikishin?s example concerning convergence in measure. We also show that affine systems fun(x)g1 n=0 generated by any Lipchitz function u(x) are Besselian.

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