Beurling type invariant subspaces on Hardy and Bergman spaces of the unit ball or polydisk

被引：0

作者：

Gu, Caixing ^{[1
]}

Luo, Shuaibing ^{[2
]}

Ma, Pan ^{[3
]}

机构：

[1] Calif Polytech State Univ San Luis Obispo, Dept Math, San Luis Obispo, CA 93407 USA

[2] Hunan Univ, Sch Math, Changsha 410082, Peoples R China

[3] Cent South Univ, Sch Math & Stat, HNP LAMA, Changsha 410083, Peoples R China

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2025年 / 68卷 / 01期

关键词：

Invariant subspace; Beurling's theorem; reproducing kernel Hilbert space on unit ball; polydisk or polyball; doubly commuting; REPRODUCING KERNELS; WANDERING SUBSPACES; THEOREM; SUBMODULES; DILATIONS; MODULE; MODELS;

D O I：

10.4153/S0008439524000535

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

McCullough and Trent generalize Beurling-Lax-Halmos invariant subspace theorem for the shift on Hardy space of the unit disk to the multi-shift on Drury-Arveson space of the unit ball by representing an invariant subspace of the multi-shift as the range of a multiplication operator that is a partial isometry. By using their method, we obtain similar representations for a class of invariant subspaces of the multi-shifts on Hardy and Bergman spaces of the unit ball or polydisk. Our results are surprisingly general and include several important classes of invariant subspaces on the unit ball or polydisk.

引用

页码：232 / 245

页数：14

共 38 条

[21] Factorizations of Kernels and Reproducing Kernel Hilbert Spaces [J].

Kumari, Rani ;

Sarkar, Jaydeb ;

Sarkar, Srijan ;

Timotin, Dan .

INTEGRAL EQUATIONS AND OPERATOR THEORY, 2017, 87 (02) :225-244

[22] THE VALIDITY OF BEURLING THEOREMS IN POLYDISCS [J].

MANDREKAR, V .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1988, 103 (01) :145-148

[23] Bergman-type reproducing kernels, contractive divisors, and dilations [J].

McCullough, S ;

Richter, S .

JOURNAL OF FUNCTIONAL ANALYSIS, 2002, 190 (02) :447-480

[24] Invariant subspaces and Nevanlinna-Pick kernels [J].

McCullough, S ;

Trent, TT .

JOURNAL OF FUNCTIONAL ANALYSIS, 2000, 178 (01) :226-249

[25] STANDARD MODELS FOR SOME COMMUTING MULTIOPERATORS [J].

MULLER, V ;

VASILESCU, FH .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1993, 117 (04) :979-989

[26] A characteristic operator function for the class of n-hypercontractions [J].

Olofsson, Anders .

JOURNAL OF FUNCTIONAL ANALYSIS, 2006, 236 (02) :517-545

[27]

Paulsen Vern I, 2016, Cambridge Studies in Advanced Mathematics, V152, DOI [10.1017/CBO9781316219232, DOI 10.1017/CBO9781316219232]

[28] IDEALS OF SQUARE SUMMABLE POWER-SERIES IN SEVERAL VARIABLES [J].

RADLOW, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 38 (02) :293-297

[29] INVARIANT SUBSPACES IN BERGMAN SPACE OVER THE BIDISC [J].

Redett, David ;

Tung, James .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 2010, 138 (07) :2425-2430

[30] INVARIANT SUBSPACES OF THE DIRICHLET SHIFT [J].

RICHTER, S .

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1988, 386 :205-220

← 1 2 3 4 →