<abstract xmlns="http://www.w3.org/1999/xhtml">We give a sufficient condition for coefficients of double series Σ Σ<italic>n</italic>,<italic>m</italic><italic>an,m</italic> χ<italic>n,m</italic> with respect to Vilenkin system to be convergent to zero when <italic>n</italic> + <italic>m</italic> → ∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its sum.</abstract>

We give a sufficient condition for coefficients of double series Σ Σn,man,m χn,m with respect to Vilenkin system to be convergent to zero when n + m → ∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its sum.

On the Coefficients of Multiple Series with Respect to Vilenkin System

Department of Mathematics and Computer Sciences

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

{"article-title":"On the Coefficients of Multiple Series with Respect to Vilenkin System"}

We give a sufficient condition for coefficients of double series Σ Σn,man,m χn,m with respect to Vilenkin system to be convergent to zero when n + m → ∞. This...

On the Coefficients of Multiple Series with Respect to Vilenkin System

Published Online: Nov 18, 2017

Page range: 81 - 92

Received: Nov 11, 2016

DOI: https://doi.org/10.1515/tmmp-2017-0007

Keywords
Vilenkin system, multiple Vilenkin series, rectangular convergence, Perron integral, Saks continuity, recovering the coefficients

© 2017 Valentin A. Skvortsov et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

On the Coefficients of Multiple Series with Respect to Vilenkin System

Published Online: Nov 18, 2017

Page range: 81 - 92

Received: Nov 11, 2016

DOI: https://doi.org/10.1515/tmmp-2017-0007

KeywordsVilenkin system, multiple Vilenkin series, rectangular convergence, Perron integral, Saks continuity, recovering the coefficients

© 2017 Valentin A. Skvortsov et al., published by De Gruyter Open

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
Vilenkin system, multiple Vilenkin series, rectangular convergence, Perron integral, Saks continuity, recovering the coefficients