A Product Formula for Homogeneous Characteristic Functions

Bagchi, Bhaskar; Hazra, Somnath; Misra, Gadadhar

doi:10.1007/s00020-023-02730-x

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Decomposition Of π1

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2024

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“…To determine among the kernels described in Theorem 3.7 (respectively, Theorem 3.11), the ones that are nonnegative definite, we recall a slight generalization of the criterion for nonnegative definiteness of Farut-Koranyi [9, Lemma 5.4]: Lemma 3.12 (Lemma 5.1 of [4]). Let Ω be a domain in ℂ 𝑑 .…”

Section: Decomposition Of πmentioning

confidence: 99%

Commuting tuple of multiplication operators homogeneous under the unitary group

Ghara,

Kumar,

Misra

et al. 2024

Journal of London Math Soc

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Let be the group of unitary matrices. We find conditions to ensure that a ‐homogeneous ‐tuple is unitarily equivalent to multiplication by the coordinate functions on some reproducing kernel Hilbert space , . We describe this class of ‐homogeneous operators, equivalently, nonnegative kernels quasi‐invariant under the action of . We classify quasi‐invariant kernels transforming under with two specific choice of multipliers. A crucial ingredient of the proof is that the group has exactly two inequivalent irreducible unitary representations of dimension and none in dimensions , . We obtain explicit criterion for boundedness, reducibility, and mutual unitary equivalence among these operators.

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Section: Decomposition Of πmentioning

confidence: 99%