Monotone Sequences and the Lorentz Theorem

The properties of -monotone sequences are studied. A relationship between -monotonicity and the limiting rate of change of coefficients is revealed. Operations on sequences that do not lead out of the class are discussed. An analogue of the Lorentz theorem for trigonometric series with coefficients...

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Bibliographic Details
Published in:Moscow University mathematics bulletin 2023, Vol.78 (2), p.95-99
Main Authors: Alferova, E. D., Dyachenko, M. I.
Format: Article
Language:English
Subjects:
Analysis
Mathematics
Mathematics and Statistics
Sequences
Theorems
Online Access:Get full text
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Summary:The properties of -monotone sequences are studied. A relationship between -monotonicity and the limiting rate of change of coefficients is revealed. Operations on sequences that do not lead out of the class are discussed. An analogue of the Lorentz theorem for trigonometric series with coefficients from the classes for is proved.
ISSN:0027-1322
1934-8444
DOI:10.3103/S002713222302002X