Commuting tuple of multiplication operators homogeneous under the unitary group

被引：1

作者：

Ghara, Soumitra ^{[1
]}

Kumar, Surjit ^{[2
]}

Misra, Gadadhar ^{[3
,4
]}

Pramanick, Paramita ^{[5
]}

机构：

[1] Indian Inst Technol Kharagpur, Dept Math, Kharagpur, India

[2] Indian Inst Technol Madras, Dept Math, Chennai 600036, India

[3] Indian Stat Inst, Stat & Math Unit, Bangalore, India

[4] Indian Inst Technol, Dept Math, Gandhinagar, India

[5] Indian Inst Technol Kanpur, Dept Math & Stat, Kanpur, India

来源：

JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES | 2024年 / 109卷 / 04期

关键词：

KERNELS; SPACES;

D O I：

10.1112/jlms.12890

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let U(d) be the group of d x d unitary matrices. We find conditions to ensure that a U(d)-homogeneous d-tuple T is unitarily equivalent to multiplication by the coordinate functions on some reproducing kernel Hilbert space H-K(B-d, C-n)subset of Hol (B-d, C-n), n=dim boolean AND(d)(j=1 )ker T-& lowast; (j). We describe this class of U(d)-homogeneous operators, equivalently, non-negative kernels K quasi-invariant under the action of U(d). We classify quasi-invariant kernels K transforming under U(d) with two specific choice of multipliers. A crucial ingredient of the proof is that the group SU(d) has exactly two inequivalent irreducible unitary representations of dimension d and none in dimensions 2,& mldr;,d-1, d >= 3. We obtain explicit criterion for boundedness, reducibility and mutual unitary equivalence among these operators

引用

页数：37