Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

Lopushansky, Oleh

doi:10.1007/s00025-017-0750-0

Cited by 2 publications

(3 citation statements)

References 22 publications

(17 reference statements)

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“…with h ∈ H. Finally note that this work is a significant extension of the previous publication [13]. The newness results from the observation that the system of Schur polynomials with variables on Paley-Wiener maps forms an orthonormal basis in the space L 2 χ .…”

Section: Introductionmentioning

confidence: 72%

Weyl–Schrödinger Representations of Heisenberg Groups in Infinite Dimensions

Lopushansky

2020

Results Math

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A complexified Heisenberg matrix group H C with entries from an infinitedimensional Hilbert space H is investigated. The Weyl-Schrödinger type irreducible representations of H C on the space L 2 χ of square-integrable scalar functions is described. The integrability is understood under the invariant probability measure χ which satisfies an abstract Kolmogorov consistency conditions over the infinite-dimensional unitary group U (∞) irreducible acted on H. The space L 2 χ is generated by Schur polynomials in variables on Paley-Wiener maps over U (∞). Therewith, the Fourier-image of L 2 χ coincides with a space of Hilbert-Schmidt entire analytic functions on H generated by suitable Fock space. Applications to linear and nonlinear heat equations over the group H C are considered.

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Section: Introductionmentioning

confidence: 72%

Weyl–Schrödinger Representations of Heisenberg Groups in Infinite Dimensions

Lopushansky

2020

Results Math

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“…where χ ∅ ı = 1, form orthogonal bases in H with summation over all semistandard Young tabloids [ı λ ] such that ı λ ⊢ n. The function p ψ is entire Hilbert-Schmidt analytic [9, n.5], [8].…”

Section: Hardy Spaces Of Hilbert-schmidt Analytic Functionsmentioning

confidence: 99%

“…The case of Weyl-Schrödinger representation in infinite dimensions was also analyzed in [8]. The currently analyzed case is its natural complement because the group U(∞) is totally embedded into the operator * -algebra E hs .…”

Section: Introductionmentioning

confidence: 99%

Weyl-Schrödinger representations of infinite-dimensional Heisenberg groups on symmetric Wiener spaces

Lopushansky¹

2017

Preprint

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An infinite-dimensional version of the Heisenberg matrix group, consisting of entries from an algebra of Hilbert-Schmidt operators, is investigated. We find its irreducible Weyl-Schrödinger type representation on a symmetric Wiener space. This space is generated by symmetric Schur polynomials in variables on Paley-Wiener maps with well-defined Fourier transforms in relative to an invariant probability measure over the infinite-dimensional unitary group. Intertwining properties of such Fourier transforms under shift and multiplicative groups are investigated.

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Paley-Wiener Isomorphism Over Infinite-Dimensional Unitary Groups

Cited by 2 publications

References 22 publications

Weyl–Schrödinger Representations of Heisenberg Groups in Infinite Dimensions

Weyl–Schrödinger Representations of Heisenberg Groups in Infinite Dimensions

Weyl-Schrödinger representations of infinite-dimensional Heisenberg groups on symmetric Wiener spaces

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