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On a function system making a basis in a weight space


Abstract

We find necessary and sufficient conditions for systems of functions generated by a second order differential equation to form a basis. The results are applied to show that Mathieu functions make a basis.

Key words: Basis, non-selfadjoint operator, the Muckenhaupt condition.


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Article Information

TitleOn a function system making a basis in a weight space
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 3, 261-269
MilestonesReceived 11/05/2017; Revised 23/06/2017
CopyrightThe Author(s) 2017 (CC BY-SA)

Authors Information

V. A. Zolotarev
Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkov, Ukraine
V. N. Karazin Kharkov National University, Kharkov, Ukraine

V. N. Levchuk
Poltava National Technical Yuri Kondratyuk University, Poltava, Ukraine


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Citation Example

V. A. Zolotarev and V. N. Levchuk, On a function system making a basis in a weight space, Methods Funct. Anal. Topology 23 (2017), no. 3, 261-269.


BibTex

@article {MFAT987,
    AUTHOR = {Zolotarev, V. A. and Levchuk, V. N.},
     TITLE = {On a function system making a basis in a weight space},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {23},
      YEAR = {2017},
    NUMBER = {3},
     PAGES = {261-269},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=987},
}


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