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<p>We show that there exists a unique non-trivial separable Hilbert space of analytic functions on <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {C}^{2n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">C</mi> </mrow> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msup> </math></EquationSource> </InlineEquation> for which certain irreducible unitary representations of the twisted Heisenberg group act in a uniformly bounded manner. Moreover, we prove Sarason’s product problem for twisted Fock spaces, which are non-radial weighted spaces distinct from conventional Fock and Fock-Sobolev spaces.</p>

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Non-isometric invariance of twisted Fock spaces and Sarason’s product problem

  • 期刊论文

  • 发表日期：

    2026年7月13日

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  • Ankush Ghartan,
  • D. Venku Naidu

摘要

We show that there exists a unique non-trivial separable Hilbert space of analytic functions on \(\mathbb {C}^{2n}\) C 2 n for which certain irreducible unitary representations of the twisted Heisenberg group act in a uniformly bounded manner. Moreover, we prove Sarason’s product problem for twisted Fock spaces, which are non-radial weighted spaces distinct from conventional Fock and Fock-Sobolev spaces.