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Izvestiya: Mathematics, 2008, Volume 72, Issue 5, Pages 915–976
DOI: https://doi.org/10.1070/IM2008v072n05ABEH002424 (Mi im2680) 		 
This article is cited in 11 scientific papers (total in 12 papers)

Harmonic analysis on local fields and adelic spaces. I

D. V. Osipov, A. N. Parshin

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (664 kB) Citations (12) Russian version article
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DOI: https://doi.org/10.1070/IM2008v072n05ABEH002424
Abstract: We develop harmonic analysis on the objects of a category $C_2$ of infinite-dimensional filtered vector spaces over a finite field. This category includes two-dimensional local fields and adelic spaces of algebraic surfaces defined over a finite field. As the main result, we construct the theory of the Fourier transform on these objects and obtain two-dimensional Poisson formulae.
Received: 20.06.2007
Bibliographic databases:
Document Type: Article
UDC: 512.75
MSC: 11R56, 18B30, 43A80
Language: English
Original paper language: Russian
Citation: D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. I”, Izv. Math., 72:5 (2008), 915–976
Citation in format AMSBIB
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\paper Harmonic analysis on local fields and adelic spaces.~I
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\vol 72
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\pages 915--976
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  • https://doi.org/10.1070/IM2008v072n05ABEH002424
  • https://www.mathnet.ru/eng/im/v72/i5/p77
    Cycle of papers
    This publication is cited in the following 12 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
     
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