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Izv. RAN. Ser. Mat., 2008, Volume 72, Issue 5, Pages 77–140 (Mi izv2680)  

This article is cited in 9 scientific papers (total in 10 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.

DOI: https://doi.org/10.4213/im2680

Full text: PDF file (1002 kB)
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English version:
Izvestiya: Mathematics, 2008, 72:5, 915–976

Bibliographic databases:

Document Type: Article
UDC: 512.75
MSC: 11R56, 18B30, 43A80
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

Citation in format AMSBIB
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    This publication is cited in the following articles:
    1. D. V. Osipov, A. N. Parshin, “Harmonic analysis on local fields and adelic spaces. II”, Izv. Math., 75:4 (2011), 749–814  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    2. A. N. Parshin, “Notes on the Poisson formula”, St. Petersburg Math. J., 23:5 (2012), 781–818  mathnet  crossref  mathscinet  isi  elib  elib
    3. Previdi L., “Locally compact objects in exact categories”, Internat. J. Math., 22:12 (2011), 1787–1821  crossref  mathscinet  zmath  isi  elib  scopus
    4. Osipov D.V., Parshin A.N., “Harmonic analysis and the Riemann-Roch theorem”, Dokl. Math., 84:3 (2011), 826–829  crossref  mathscinet  zmath  isi  elib  elib  scopus
    5. Liu D., “Theta functions and arithmetic quotients of loop groups”, Math. Res. Lett., 19:1 (2012), 13–29  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    6. S. V. Vostokov, S. O. Gorchinskiy, A. B. Zheglov, Yu. G. Zarkhin, Yu. V. Nesterenko, D. O. Orlov, D. V. Osipov, V. L. Popov, A. G. Sergeev, I. R. Shafarevich, “Aleksei Nikolaevich Parshin (on his 70th birthday)”, Russian Math. Surveys, 68:1 (2013), 189–197  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    7. Alberto Cámara, “Locally convex structures on higher local fields”, Journal of Number Theory, 2014  crossref  mathscinet  scopus
    8. Ivan Fesenko, “Geometric adeles and the Riemann–Roch theorem for $1$-cycles on surfaces”, Mosc. Math. J., 15:3 (2015), 435–453  mathnet  mathscinet
    9. D. V. Osipov, A. N. Parshin, “Representations of the discrete Heisenberg group on distribution spaces of two-dimensional local fields”, Proc. Steklov Inst. Math., 292 (2016), 185–201  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    10. Liu D. Zhu Y., “Lca(2), Weil Index, and Product Formula”, Adv. Math., 329 (2018), 1088–1136  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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