Cross-Toeplitz Operators on the Fock--Segal--Bargmann Spaces and Two-Sided Convolutions on the Heisenberg Group
| Autor: | Kisil, Vladimir V. |
|---|---|
| Rok vydání: | 2021 |
| Předmět: | |
| Zdroj: | Ann. Funct. Anal. (2023) 14:38 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1007/s43034-022-00249-7 |
| Popis: | We introduce an extended class of cross-Toeplitz operators which act between Fock--Segal--Bargmann spaces with different weights. It is natural to consider these operators in the framework of representation theory of the Heisenberg group. Our main technique is representation of cross-Toeplitz by two-sided relative convolutions from the Heisenberg group. In turn, two-sided convolutions are reduced to usual (one-sided) convolutions on the Heisenberg group of the doubled dimensionality. This allows us to utilise the powerful group-representation technique of coherent states, co- and contra-variant transforms, twisted convolutions, symplectic Fourier transform, etc.We discuss connections of (cross-)Toeplitz operators with pseudo-differential operators, localisation operators in time-frequency analysis, and characterisation of kernels in terms of ladder operators. The paper is written in detailed and reasonably self-contained manner to be suitable as an introduction into group-theoretical methods in phase space and time-frequency operator theory. Comment: 45 p., AMS-LateX, 3 PDF images in two figures; v2&v3: minor corrections |
| Databáze: | arXiv |
| Externí odkaz: |
|