| 1. |
- Aleman, Alexandru, et al.
(författare)
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Backward Shift and Nearly Invariant Subspaces of Fock-type Spaces
- 2022
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Ingår i: International mathematics research notices. - : Oxford University Press (OUP). - 1073-7928 .- 1687-0247. ; 2022:10, s. 7390-7419
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Tidskriftsartikel (refereegranskat)abstract
- We study the structure of the backward shift invariant and nearly invariant subspaces in weighted Fock-type spaces ℱWp, whose weight is not necessarily radial. We show that in the spaces ℱWp, which contain the polynomials as a dense subspace (in particular, in the radial case), all nontrivial backward shift invariant subspaces are of the form ℘n, that is, finite-dimensional subspaces consisting of polynomials of degree at most n. In general, the structure of the nearly invariant subspaces is more complicated. In the case of spaces of slow growth (up to zero exponential type), we establish an analogue of de Branges' ordering theorem. We then construct examples that show that the result fails for general Fock-type spaces of larger growth.
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| 2. |
- Aleman, Alexandru, et al.
(författare)
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Density of disk algebra functions in de Branges–Rovnyak spaces
- 2017
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Ingår i: Comptes rendus. Mathematique. - : Elsevier BV. - 1631-073X .- 1778-3569. ; 355:8, s. 871-875
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Tidskriftsartikel (refereegranskat)abstract
- We prove that functions analytic in the unit disk and continuous up to the boundary are dense in the de Branges–Rovnyak spaces induced by the extreme points of the unit ball of . Together with previous theorems, it follows that this class of functions is dense in any de Branges–Rovnyak space.
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| 3. |
- Aleman, Alexandru, et al.
(författare)
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Hilbert spaces of analytic functions with a contractive backward shift
- 2019
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Ingår i: Journal of Functional Analysis. - : Elsevier BV. - 0022-1236 .- 1096-0783. ; 277:1, s. 157-199
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Tidskriftsartikel (refereegranskat)abstract
- We consider Hilbert spaces of analytic functions in the disk with a normalized reproducing kernel and such that the backward shift is a contraction on the space. We present a model for this operator and use it to prove the surprising result that functions which extend continuously to the closure of the disk are dense in the space. This has several applications, for example we can answer a question regarding reverse Carleson embeddings for these spaces. We also identify a large class of spaces which are similar to the de Branges–Rovnyak spaces and prove some results which are new even in the classical case.
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| 4. |
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| 5. |
- Nedic, Mitja, 1990-
(författare)
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Integral representations of Herglotz-Nevanlinna functions
- 2017
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Licentiatavhandling (övrigt vetenskapligt/konstnärligt)abstract
- In this thesis, we study integral representations of Herglotz-Nevanlinna functions, that is to say holomorphic functions defined on a product of several copies of the complex upper half-plane having non-negative imaginary part. The manuscript is divided into three parts, beginning with a general introduction followed by two papers.In the general introduction, we familiarize ourselves with the concept of a Herglotz-Nevanlinna function as well as providing a comprehensive introduction into the theory of integral representations for this particular class of functions.Paper I treats exclusively the two-variable case and presents an integral representation of Herglotz-Nevanlinna functions in two complex variables in terms of a real number, two non-negative numbers and a positive Borel measure satisfying two properties. Three properties that hold for the class of measures appearing in such integral representations are also proven.In Paper II, we provide an integral representation for the class of Herglotz-Nevanlinna functions in arbitrarily many complex variables in terms of a real number, a linear term and a positive Borel measure satisfying two properties. Properties of the class of measures appearing in this representation are then discussed in detail as well as alternative descriptions of said class. Finally, a symmetry formula satisfied by Herglotz-Nevanlinna functions is proved at the end.
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| 6. |
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| 7. |
- Aleman, Alexandru, et al.
(författare)
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A Quantitative Estimate for Bounded Point Evaluations in P-t(mu)-spaces
- 2010
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Ingår i: Topics In Operator Theory: Operators, Matrices And Analytic Functions, Vol 1. - 0255-0156. ; 202, s. 1-10
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Konferensbidrag (refereegranskat)abstract
- In this note we explain how X. Tolsa's work on analytic capacity and an adaptation of Thomson's coloring scheme can be used to obtain a quantitative version of J. Thomson's theorem on bounded point evaluations for P-t(mu)-spaces.
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| 8. |
- Aleman, Alexandru, et al.
(författare)
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An Hp scale for complete Pick spaces
- 2021
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Ingår i: Studia Mathematica. - 0039-3223. ; 258:3, s. 343-359
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Tidskriftsartikel (refereegranskat)abstract
- We define by interpolation a scale analogous to the Hardy Hp scale for complete Pick spaces, and establish some of the basic properties of the resulting spaces, which we call Hp. In particular, we obtain an Hp-Hq duality and establish sharp pointwise estimates for functions in Hp
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| 9. |
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| 10. |
- Aleman, Alexandru, et al.
(författare)
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Analytic contractions and boundary behaviour -- an overview.
- 2006
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Ingår i: Proceedings of the first advanced course in operator theory and complex analysis, University of Sevilla, Sevilla, Spain, June 2004.. - 8447210243 ; , s. 3-26
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Konferensbidrag (refereegranskat)
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