New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis

K. Groechenig

doi:10.5802/jolt.1191

K. Groechenig

Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 659-680

Abstract

We study function spaces that are related to square-integrable, irreducible, unitary representations of several low-dimensional nilpotent Lie groups. These are new examples of coorbit theory and yield new families of function spaces on R^d. The concrete realization of the representation suggests that these function spaces are useful for generalized time-frequency analysis or phase-space analysis.

arXiv Zbl

DOI: 10.5802/jolt.1191

Classification: 22E25, 42B35, 46E35
Keywords: Nilpotent Lie group, square-integrable representation modulo center, coorbit space, modulation space, time-frequency analysis, chirp, frame

@article{JOLT_2021_31_3_a3,
     author = {K. Groechenig},
     title = {New {Function} {Spaces} {Associated} to {Representations} of {Nilpotent} {Lie} {Groups} and {Generalized} {Time-Frequency} {Analysis}},
     journal = {Journal of Lie Theory},
     pages = {659--680},
     year = {2021},
     volume = {31},
     number = {3},
     doi = {10.5802/jolt.1191},
     zbl = {1486.22010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1191/}
}

TY  - JOUR
AU  - K. Groechenig
TI  - New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis
JO  - Journal of Lie Theory
PY  - 2021
SP  - 659
EP  - 680
VL  - 31
IS  - 3
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.1191/
DO  - 10.5802/jolt.1191
ID  - JOLT_2021_31_3_a3
ER  -

%0 Journal Article
%A K. Groechenig
%T New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis
%J Journal of Lie Theory
%D 2021
%P 659-680
%V 31
%N 3
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.1191/
%R 10.5802/jolt.1191
%F JOLT_2021_31_3_a3

K. Groechenig. New Function Spaces Associated to Representations of Nilpotent Lie Groups and Generalized Time-Frequency Analysis. Journal of Lie Theory, Volume 31 (2021) no. 3, pp. 659-680. doi: 10.5802/jolt.1191

Cited by Sources: