ZERO-BASED INVARIANT SUBSPACES IN THE BERGMAN SPACE

Yıl 2018, Cilt: 67 Sayı: 1, 277 - 285, 01.02.2018

Bouabdallah Fatıha Bendaoud Zohra

https://doi.org/10.1501/Commua1_0000000849

Cited By: 1

Öz

It is known that Beurling’s theorem concerning invariant subspaces is not true in the Bergman space (in contrast to the Hardy space case).However, Aleman, Richter, and Sundberge proved that every cyclic invariantasubspace in the Bergman space Lp(D), 0 < p < +1, is generated by its extremal function. This implies, in particular, that for every zero-based invariantsubspace in the Bergman space the Beurling’s theorem stands true. Here, wecalculate the reproducing kernel of the zero-based invariant subspace Mninathe Bergman space L2(D) where the associated wandering subspace Mnis one-dimensional, and spanned by the unit vector Gn(z) =zMn p n + 1zn

Anahtar Kelimeler

Bergman space, inner function, Beurling’s theorem, kernel function

Kaynakça

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• University, ALGERIA E-mail address : [e-mail] ORCID: http://orcid.org/0000-0002-4890-3386 Current address : Bendaoud Zohra: Laboratory of Pure and Applied Mathematics, Laghouat
• University, ALGERIA E-mail address : [e-mail]