数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (2): 293-300.doi: 10.1016/S0252-9602(17)30002-4

• 论文 •    下一篇

ON THE FOURIER-VILENKIN COEFFICIENTS

Martin G. GRIGORYAN, Stepan SARGSYAN   

  1. Chair of Higher Mathematics, Faculty of Physics, Yerevan State University, Alex Manoogyan str. 1, 0025, Yerevan, Republic of Armenia
  • 收稿日期:2014-12-03 修回日期:2016-06-07 出版日期:2017-04-25 发布日期:2017-04-25
  • 作者简介:Martin G. GRIGORYAN,E-mail:gmarting@ysu.am;Stepan SARGSYAN,E-mail:stepansargsyan@ysu.am
  • 基金资助:

    This work was supported by State Committee Science MES RA, in frame of the research project N SCS 13-1A313.

ON THE FOURIER-VILENKIN COEFFICIENTS

Martin G. GRIGORYAN, Stepan SARGSYAN   

  1. Chair of Higher Mathematics, Faculty of Physics, Yerevan State University, Alex Manoogyan str. 1, 0025, Yerevan, Republic of Armenia
  • Received:2014-12-03 Revised:2016-06-07 Online:2017-04-25 Published:2017-04-25
  • Supported by:

    This work was supported by State Committee Science MES RA, in frame of the research project N SCS 13-1A313.

摘要:

In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems:for any ε ∈(0,1), there exists a measurable set E ∈[0,1) of measure bigger than 1-ε such that for any function fL1[0,1), it is possible to find a function gL1[0,1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing.

关键词: Vilenkin system, expansions, Fourier coefficients

Abstract:

In this article, we prove the following statement that is true for both unbounded and bounded Vilenkin systems:for any ε ∈(0,1), there exists a measurable set E ∈[0,1) of measure bigger than 1-ε such that for any function fL1[0,1), it is possible to find a function gL1[0,1) coinciding with f on E and the absolute values of non zero Fourier coefficients of g with respect to the Vilenkin system are monotonically decreasing.

Key words: Vilenkin system, expansions, Fourier coefficients