Spectral Synthesis on the Reduced Heisenberg Group

The spectral synthesis problem for the phase space associated with the reduced Heisenberg group is studied. The paper deals with the case of subspaces in invariant under the twisted shifts and the action of the unitary group . It is shown that any such subspace is generated by the root vectors of a...

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Bibliographic Details
Published in:Mathematical Notes 2023-02, Vol.113 (1-2), p.49-58
Main Authors: Volchkov, V. V., Volchkov, Vit. V.
Format: Article
Language:English
Subjects:
14/34
639/766/189
639/766/530
639/766/747
Invariants
Mathematics
Mathematics and Statistics
Subspaces
Synthesis
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Summary:The spectral synthesis problem for the phase space associated with the reduced Heisenberg group is studied. The paper deals with the case of subspaces in invariant under the twisted shifts and the action of the unitary group . It is shown that any such subspace is generated by the root vectors of a special Hermite operator contained in this subspace. As a corollary, we obtain the spectral synthesis theorem for subspaces in invariant under the unilateral shifts and the action of the unitary group .
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434623010066