Detailed Information on Publication Record
2023
A family of homogeneous operators in the Cowen-Douglas class over the poly-disc
DEB, Prahllad and Somnath HAZRABasic 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:
RIV identification code
RIV/47813059:19610/23:A0000129
Organization unit
Mathematical Institute in Opava
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.