Open AccessAffine Bessel sequences and Nikishin’s example
Author(s) -
В. А. Миронов,
Abdizhahan Manapoly 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.