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Heat kernel analysis for Bessel operators on symmetric cones

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Heat kernel analysis for Bessel operators on symmetric cones. / Möllers, Jan.

I: Journal of Lie Theory, Bind 24, Nr. 2, 2014, s. 373-396.

Publikation: Bidrag til tidsskrift/Konferencebidrag i tidsskrift /Bidrag til avisTidsskriftartikelForskningpeer review

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Möllers J. 2014. Heat kernel analysis for Bessel operators on symmetric cones. Journal of Lie Theory. 24(2):373-396.

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Möllers, Jan. / Heat kernel analysis for Bessel operators on symmetric cones. I: Journal of Lie Theory. 2014 ; Bind 24, Nr. 2. s. 373-396.

Bibtex

@article{ade6601ea15347dd8c7a406bf27930f9,
title = "Heat kernel analysis for Bessel operators on symmetric cones",
abstract = "We investigate the heat equation corresponding to the Bessel operators on a symmetric cone $Ω=G/K$. These operators form a one-parameter family of elliptic self-adjoint second order differential operators and occur in the Lie algebra action of certain unitary highest weight representations. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space on the complexification $G_{\mathbb C}/K_{\mathbb C}$ of $Ω$, the weight being expressed explicitly in terms of a multivariable $K$-Bessel function on $Ω$. Even in the special case of the symmetric cone $Ω=\mathbb{R}_+$ these results seem to be new.",
author = "Jan M{\"o}llers",
year = "2014",
language = "English",
volume = "24",
pages = "373--396",
journal = "Journal of Lie Theory",
issn = "0949-5932",
publisher = "Heldermann Verlag",
number = "2",

}

RIS

TY - JOUR

T1 - Heat kernel analysis for Bessel operators on symmetric cones

AU - Möllers, Jan

PY - 2014

Y1 - 2014

N2 - We investigate the heat equation corresponding to the Bessel operators on a symmetric cone $Ω=G/K$. These operators form a one-parameter family of elliptic self-adjoint second order differential operators and occur in the Lie algebra action of certain unitary highest weight representations. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space on the complexification $G_{\mathbb C}/K_{\mathbb C}$ of $Ω$, the weight being expressed explicitly in terms of a multivariable $K$-Bessel function on $Ω$. Even in the special case of the symmetric cone $Ω=\mathbb{R}_+$ these results seem to be new.

AB - We investigate the heat equation corresponding to the Bessel operators on a symmetric cone $Ω=G/K$. These operators form a one-parameter family of elliptic self-adjoint second order differential operators and occur in the Lie algebra action of certain unitary highest weight representations. The heat kernel is explicitly given in terms of a multivariable $I$-Bessel function on $Ω$. Its corresponding heat kernel transform defines a continuous linear operator between $L^p$-spaces. The unitary image of the $L^2$-space under the heat kernel transform is characterized as a weighted Bergmann space on the complexification $G_{\mathbb C}/K_{\mathbb C}$ of $Ω$, the weight being expressed explicitly in terms of a multivariable $K$-Bessel function on $Ω$. Even in the special case of the symmetric cone $Ω=\mathbb{R}_+$ these results seem to be new.

M3 - Journal article

VL - 24

SP - 373

EP - 396

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 2

ER -