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Izvestiya: Mathematics, 2011, Volume 75, Issue 4, Pages 749–814
DOI: https://doi.org/10.1070/IM2011v075n04ABEH002552 (Mi im4278) 		 
This article is cited in 19 scientific papers (total in 20 papers)

Harmonic analysis on local fields and adelic spaces. II

D. V. Osipov, A. N. Parshin

Steklov Mathematical Institute, Russian Academy of Sciences
English version PDF (740 kB) Citations (20)
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DOI: https://doi.org/10.1070/IM2011v075n04ABEH002552
Abstract: We develop harmonic analysis in certain categories of filtered Abelian groups and vector spaces. The objects of these categories include local fields and adelic spaces arising from arithmetic surfaces. We prove some structure theorems for quotients of the adèle groups of algebraic and arithmetic surfaces.
Keywords: arithmetic surfaces, higher adèles, harmonic analysis, Fourier transform, Poisson summation formulae.
Received: 22.12.2009
Revised: 10.12.2010
Russian version:
Izvestiya Rossiiskoi Akademii Nauk. Seriya Matematicheskaya, 2011, Volume 75, Issue 4, Pages 91–164
DOI: https://doi.org/10.4213/im4278
Bibliographic databases:
Document Type: Article
UDC: 512.75
MSC: 11R56, 18B30, 43A70
Language: English
Original paper language: Russian
Citation: D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. RAN. Ser. Mat., 75:4 (2011), 91–164; Izv. Math., 75:4 (2011), 749–814
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/im/v75/i4/p91
    Cycle of papers
    This publication is cited in the following 20 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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    Abstract page:902
    Russian version PDF:222
    English version PDF:15
    References:49
    First page:11
     
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