Izvestiya of Saratov University.

Mathematics. Mechanics. Informatics

ISSN 1816-9791 (Print)
ISSN 2541-9005 (Online)


For citation:

Vodolasov A. M., Lukomskii S. F. MRA on Local Fields of Positive Characteristic. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2014, vol. 14, iss. 4, pp. 511-518. DOI: 10.18500/1816-9791-2014-14-4-511-518, EDN: TBDAFV

This is an open access article distributed under the terms of Creative Commons Attribution 4.0 International License (CC-BY 4.0).
Published online: 
01.12.2014
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Russian
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UDC: 
517.51
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TBDAFV

MRA on Local Fields of Positive Characteristic

Autors: 
Vodolasov Alexander Mikhailovich, Saratov State University
Lukomskii Sergei Feodorovich, Saratov State University
Abstract: 

We prove that the local field of positive characteristic is a vector space over a finite field.

References: 
  1. Taibleson M. H. Fourier Analysis on Local Fields. Princeton : Princeton Univ. Press, 1975.
  2. Jiang H., Li D., Jin N. Multiresolution analysis on local fields // J. Math. Anal. Appl. 2004. Vol. 294. P. 523–532.
  3. Behera B., Jahan Q. Multiresolution analysis on local fields and characterization of scaling functions // Adv. Pure Appl. Math. 2012. Vol. 3. P. 181–202.
  4. Behera B, Jahan Q. Biorthogonal Wavelets on Local Fields of Positive Characteristic // Communications in Math. Anal. 2013. Vol. 15, № 2. P. 52–75.
  5. Behera B, Jahan Q. Wavelet packets and wavelet frame packets on local fields of positive characteristic // J. Math. Anal. Appl. 2012. Vol. 395. P. 1–14.
  6. Лидл Р., Нидеррайтер Г. Конечные поля : в 2 т. М. : Мир, 1988.
  7. Гельфанд И. М., Граев М. И., ПятецкийШапиро И. И. Теория представлений и автоморфные функции. М. : Наука, 1966.
  8. Lukomskii S. F. Step refinable functions and orthogonal MRA on Vilenkin groups // J. Fourier Anal. Appl. 2014. Vol. 20, № 1. P. 42–65.
  9. Lukomskii S. F. Trees in Wavelet analysis on Vilenkin groups. Preprint arxiv.org/abs/1303.5635.
  10. Фарков Ю. А. Ортогональные вейвлеты на прямых произведениях циклических групп // Матем. заметки. 2007. Т. 82, № 6. С. 934–952. DOI: 10.4213/mzm4181.
Received: 
11.06.2014
Accepted: 
26.10.2014
Published: 
01.12.2014