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Harmonic analysis on local fields and adelic spaces. II. (English. Russian original) Zbl 1232.11122
Izv. Math. 75, No. 4, 749-814 (2011); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 75, No. 4, 91-164 (2011).
The paper under review is in continuation to [Izv. Math. 72, No. 5, 915–976 (2008); translation from Izv. Ross. Akad. Nauk, Ser. Mat. 72, No. 5, 77–140 (2008; Zbl 1222.11137)]. It is concerned with the development of harmonic analysis in certain categories of filtered abelian groups and vector spaces. This theory is then used to study arithmetic surfaces. Some examples including the case of adele groups for schemes of dimension 1 and of dimension 2 are considered.
Reviewer: V. Popa (Chisinau)

MSC:
11R56 Adèle rings and groups
18B30 Categories of topological spaces and continuous mappings (MSC2010)
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