Harmonic analysis on the rank-2 value group of a two-dimensional local field. (English. Russian original) Zbl 1452.43005
Sb. Math. 211, No. 1, 115-160 (2020); translation from Mat. Sb. 211, No. 1, 125-174 (2020).
Summary: In this work we construct a harmonic analysis on free Abelian groups of rank 2, namely: we construct and investigate spaces of functions and distributions, Fourier transforms and actions of discrete and extended discrete Heisenberg groups. In the case of the rank-2 value group of a two-dimensional local field with finite last residue field we connect this harmonic analysis with harmonic analysis on the two-dimensional local field, where the latter harmonic analysis was constructed in earlier works by the authors.
MSC:
| 43A70 | Analysis on specific locally compact and other abelian groups |
| 11S80 | Other analytic theory (analogues of beta and gamma functions, \(p\)-adic integration, etc.) |
Keywords:
two-dimensional local field; value group; harmonic analysis; Fourier transform; discrete Heisenberg groupsReferences:
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