J 2023

A family of homogeneous operators in the Cowen-Douglas class over the poly-disc

DEB, Prahllad and Somnath HAZRA

Basic information

Original name

A family of homogeneous operators in the Cowen-Douglas class over the poly-disc

Authors

DEB, Prahllad (356 India, guarantor) and Somnath HAZRA (356 India, belonging to the institution)

Edition

Studia Mathematica, Warsaw, Poland, IMPAN - Institute of Mathematics. Polish Academy of Sciences, 2023, 0039-3223

Other information

Language

English

Type of outcome

Článek v odborném periodiku

Field of Study

10101 Pure mathematics

Country of publisher

Poland

Confidentiality degree

není předmětem státního či obchodního tajemství

References:

Studia Mathematica

RIV identification code

RIV/47813059:19610/23:A0000129

Organization unit

Mathematical Institute in Opava

DOI

http://dx.doi.org/10.4064/sm220630-10-1

UT WoS

000953362200001

Keywords in English

Cowen-Douglas class; curvature; hermitian holomorphic homogeneous vector bundles; homogeneous operators

Tags

Tags

International impact, Reviewed

Links

GA21-27941S, research and development project.
Změněno: 27/3/2024 14:26, Mgr. Aleš Ryšavý

Abstract

V originále

We construct a large family of positive definite kernels K : Dn x Dn-+ M(r, C), holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the subgroup Mob x center dot center dot center dot x Mob (n times) of the bi-holomorphic automorphism group of Dn. The adjoint of the n-tuple of the multiplication operators by the co-ordinate functions is then homogeneous with respect to this subgroup on the Hilbert space ?-lK determined by K. We show that these n-tuples are irreducible, are in the Cowen-Douglas class Br(Dn) and are mutually pairwise unitarily inequivalent.
Displayed: 24/12/2024 04:08