Аннотация:
We discuss a fine tuning of the co- and contra-variant transforms through construction of specific fiducial and reconstructing vectors. The technique is illustrated on three different forms of induced representations of the Heisenberg group. The covariant transform provides intertwining operators between pairs of representations. In particular, we obtain the Zak transform as an induced covariant transform intertwining the Schrödinger representation on L2(R) and the lattice (nilmanifold) representation on L2(T2). Induced covariant transforms in other pairs are Fock–Segal–Bargmann and theta transforms. Furthermore, we describe peelings which map the group-theoretical induced representations to convenient representation spaces of analytic functions. Finally, we provide a condition which can be imposed on the reconstructing vector in order to obtain an intertwining operator from the induced contravariant transform.
Образец цитирования:
Amerah A. Al Ameer, Vladimir V. Kisil, “Tuning Co- and Contra-Variant Transforms: the Heisenberg Group Illustration”, SIGMA, 18 (2022), 065, 21 pp.
\RBibitem{Al Kis22}
\by Amerah~A.~Al Ameer, Vladimir~V.~Kisil
\paper Tuning Co- and Contra-Variant Transforms: the Heisenberg Group Illustration
\jour SIGMA
\yr 2022
\vol 18
\papernumber 065
\totalpages 21
\mathnet{http://mi.mathnet.ru/sigma1861}
\crossref{https://doi.org/10.3842/SIGMA.2022.065}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=4475347}
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Эта публикация цитируется в следующих 3 статьяx:
Vladimir V. Kisil, “Cross-Toeplitz operators on the Fock–Segal–Bargmann spaces and two-sided convolutions on the Heisenberg group”, Ann. Funct. Anal., 14:2 (2023)
V. V. Kisil, “Transmutations from the Covariant Transform on the Heisenberg Group and an Extended Umbral Principle”, Lobachevskii J Math, 44:8 (2023), 3384
Taghreed Alqurashi, Vladimir V. Kisil, “Metamorphism as a covariant transform for the SSR group”, Bol. Soc. Mat. Mex., 29:2 (2023)