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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
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
Citation:
D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. I”, Izv. RAN. Ser. Mat., 72:5 (2008), 77–140; Izv. Math., 72:5 (2008), 915–976
Linking options:
https://www.mathnet.ru/eng/im2680https://doi.org/10.1070/IM2008v072n05ABEH002424 https://www.mathnet.ru/eng/im/v72/i5/p77
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Abstract page: | 967 | Russian version PDF: | 284 | English version PDF: | 19 | References: | 74 | First page: | 30 |
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