ZERO-BASED INVARIANT SUBSPACES IN THE BERGMAN SPACE
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
Keywords:
Bergman space, inner function Beurling’s theorem, kernel function,
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- University, ALGERIA E-mail address : f.bouabdallah@lagh-univ.dz ORCID: http://orcid.org/0000-0002-4890-3386 Current address : Bendaoud Zohra: Laboratory of Pure and Applied Mathematics, Laghouat
- University, ALGERIA E-mail address : z.bendaoud@lagh-univ.dz
- ISSN: 1303-5991
- Yayın Aralığı: Yılda 4 Sayı
- Başlangıç: 1948
- Yayıncı: Ankara Üniversitesi
Sayıdaki Diğer Makaleler
Djalil BOUDJEHEM, Badreddine BOUDJEHEM, Belgacem MECHERI
Huanyin CHEN, Abdullah HARMANCI
Bouabdallah FATIHA, Bendaoud ZOHRA