Division subspaces and integrable kernels

Bufetov, Alexander I.; Romanov, Roman

doi:10.1112/blms.12223

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The Proof Of Theorem1

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2024

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Cited by 4 publications

(1 citation statement)

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“…Recall the explicit formulae for the functions A, B, providing an integrable structure of the kernel Π. We now use an argument from [15]. Take a point q close to p such that Π(q, q) > 0.…”

Section: The Proof Of Theoremmentioning

confidence: 99%

A palm hierarchy for determinantal point processes with the Bessel kernel

Bufetov

2017

Proc. Steklov Inst. Math.

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The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to the taking of the reduced Palm measure at infinity for our decomposing measures. The proof proceeds by finite-dimensional approximation of our measures by orthogonal polynomial ensembles. The key remark is that the taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems.

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Section: The Proof Of Theoremmentioning

confidence: 99%

A palm hierarchy for determinantal point processes with the Bessel kernel

Bufetov

2017

Proc. Steklov Inst. Math.

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Functional Description of a Class of Quasi-Invariant Determinantal Processes

Romanov

2024

Ann. Henri Poincaré

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A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, which resolves the problem of harmonic analysis on the infinite-dimensional unitary group

Bufetov

2024

St. Petersburg Math. J.

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The main result of this note is that the shift of the parameter by 1 in the parameter space of decomposing measures in the problem of harmonic analysis on the infinite-dimensional unitary group corresponds to taking the reduced Palm measure at infinity for the decomposing measures in question. The proof proceeds by finite-dimensional approximation of the measures by orthogonal polynomial ensembles. The key remark is that taking the reduced Palm measure commutes with the scaling limit transition from finite to infinite particle systems.

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Division subspaces and integrable kernels

Abstract: In this note we prove that the reproducing kernel of a Hilbert space satisfying the division property has integrable form, is locally of trace class, and the Hilbert space itself is a Hilbert space of holomorphic functions.

Cited by 4 publications

References 18 publications

A palm hierarchy for determinantal point processes with the Bessel kernel

A palm hierarchy for determinantal point processes with the Bessel kernel

Functional Description of a Class of Quasi-Invariant Determinantal Processes

A Palm hierarchy for determinantal point processes with the confluent hypergeometric kernel, which resolves the problem of harmonic analysis on the infinite-dimensional unitary group

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