Harmonic analysis on the rank-$2$ value group of a two-dimensional local field

@article{Osipov2020HarmonicAO,
  title={Harmonic analysis on the rank-\$2\$ value group of a two-dimensional local field},
  author={D. Osipov and A. Parshin},
  journal={Sbornik Mathematics},
  year={2020},
  volume={211},
  pages={115-160}
}
In this work we construct harmonic analysis on free Abelian groups of rank $2$, namely: we construct and investigate spaces of functions and distributions, Fourier transforms, actions of discrete and extended discrete Heisenberg groups. In 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… Expand
1 Citations

References

SHOWING 1-10 OF 21 REFERENCES
Representations of Higher Adelic Groups and Arithmetic
Harmonic analysis on local fields and adelic spaces. I
Notes on the Poisson formula
Higher dimensional local fields and L–functions
A holomorphic version of the Tate-Iwasawa method for unramified L-functions. I
Monoidal Categories and Multiextensions
...
1
2
3
...