Cross-Toeplitz operators on the Fock-Segal-Bargmann spaces and two-sided convolutions on the Heisenberg group

DOI10.1007/s43034-022-00249-7OpenAlexW3197024187MaRDI QIDQ2689277

G.V.P.Khmelevskaya

Publication date: 9 March 2023

Published in: Annals of Functional Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2108.13710

zbMATH Keywords

Heisenberg groupToeplitz operatorphase spacecoherent statestime-frequency analysispseudo-differential operatorslocalisation operatorsBerezin calculuscovariant and contravariant transformsFock-Segal-Bargmann spaceBerezin quantisationtwo-sided convolutions

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Toeplitz operators, Hankel operators, Wiener-Hopf operators (47B35) Coherent states (81R30) Phase-space methods including Wigner distributions, etc. applied to problems in quantum mechanics (81S30) Hilbert spaces with reproducing kernels (= (proper) functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) (46E22) (L^p)-spaces and other function spaces on groups, semigroups, etc. (43A15) Pseudodifferential operators (47G30) Linear operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) (47B32) Bergman spaces and Fock spaces (30H20)

Related Items (2)

Transmutations from the covariant transform on the Heisenberg group and an extended umbral principle ⋮ Metamorphism as a covariant transform for the SSR group

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