Author: Louis De Branges
Publisher:
ISBN:
Category : Functions, Entire
Languages : en
Pages : 344

Get Book Here

Book Description

Author: Louis De Branges de Bourcia
Publisher:
ISBN:
Category :
Languages : en
Pages : 326

Get Book Here

Book Description

Author: Javad Mashreghi
Publisher: American Mathematical Soc.
ISBN: 9780821848791
Category : Mathematics
Languages : en
Pages : 0

Get Book Here

Book Description
Hilbert spaces of analytic functions are currently a very active field of complex analysis. The Hardy space is the most senior member of this family. However, other classes of analytic functions such as the classical Bergman space, the Dirichlet space, the de Branges-Rovnyak spaces, and various spaces of entire functions, have been extensively studied. This provides an account of the latest developments in the field of analytic function theory.

Author: Jacob Korevaar
Publisher: American Mathematical Soc.
ISBN: 9780821867761
Category :
Languages : en
Pages : 564

Get Book Here

Book Description

Author: Louis De Branges
Publisher:
ISBN:
Category : Functions, Entire
Languages : en
Pages : 344

Get Book Here

Book Description

Author: Ilia Binder
Publisher: Springer Nature
ISBN: 3031392701
Category : Mathematics
Languages : en
Pages : 487

Get Book Here

Book Description
The focus program on Analytic Function Spaces and their Applications took place at Fields Institute from July 1st to December 31st, 2021. Hilbert spaces of analytic functions form one of the pillars of complex analysis. These spaces have a rich structure and for more than a century have been studied by many prominent mathematicians. They also have several essential applications in other fields of mathematics and engineering, e.g., robust control engineering, signal and image processing, and theory of communication. The most important Hilbert space of analytic functions is the Hardy class H2. However, its close cousins, e.g. the Bergman space A2, the Dirichlet space D, the model subspaces Kt, and the de Branges-Rovnyak spaces H(b), have also been the center of attention in the past two decades. Studying the Hilbert spaces of analytic functions and the operators acting on them, as well as their applications in other parts of mathematics or engineering were the main subjects of this program. During the program, the world leading experts on function spaces gathered and discussed the new achievements and future venues of research on analytic function spaces, their operators, and their applications in other domains. With more than 250 hours of lectures by prominent mathematicians, a wide variety of topics were covered. More explicitly, there were mini-courses and workshops on Hardy Spaces, Dirichlet Spaces, Bergman Spaces, Model Spaces, Interpolation and Sampling, Riesz Bases, Frames and Signal Processing, Bounded Mean Oscillation, de Branges-Rovnyak Spaces, Operators on Function Spaces, Truncated Toeplitz Operators, Blaschke Products and Inner Functions, Discrete and Continuous Semigroups of Composition Operators, The Corona Problem, Non-commutative Function Theory, Drury-Arveson Space, and Convergence of Scattering Data and Non-linear Fourier Transform. At the end of each week, there was a high profile colloquium talk on the current topic. The program also contained two semester-long advanced courses on Schramm Loewner Evolution and Lattice Models and Reproducing Kernel Hilbert Space of Analytic Functions. The current volume features a more detailed version of some of the talks presented during the program.

Author: Javad Mashreghi
Publisher: American Mathematical Soc.
ISBN: 0821870459
Category : Mathematics
Languages : en
Pages : 230

Get Book Here

Book Description

Author: Jorge-Nuno O. Silva
Publisher: Universal-Publishers
ISBN: 1581120230
Category : Mathematics
Languages : en
Pages : 31

Get Book Here

Book Description
In this work we explore the relation between some local Dirichlet spaces and some operator ranges. As an application we give numerical bounds for an equivalence of norms on a particular subspace of the Hardy space. Based on these results we introduce an operator on H^2 which we study in some detail. We also introduce a Hilbert space of analytic functions on the unit disc, prove the polynomials are dense in it, and give a characterization of its elements. On these spaces we study the action of composition operators induced by holomorphic self maps of the disc. We give characterizations of the bounded and compact ones in terms of the behavior of the inducing maps.

Author: Jacob Korevaar
Publisher: American Mathematical Soc.
ISBN: 0821814117
Category : Mathematics
Languages : en
Pages : 562

Get Book Here

Book Description

Author: Jim Agler
Publisher: American Mathematical Society
ISBN: 1470468557
Category : Mathematics
Languages : en
Pages : 330

Get Book Here

Book Description
The book first rigorously develops the theory of reproducing kernel Hilbert spaces. The authors then discuss the Pick problem of finding the function of smallest $H^infty$ norm that has specified values at a finite number of points in the disk. Their viewpoint is to consider $H^infty$ as the multiplier algebra of the Hardy space and to use Hilbert space techniques to solve the problem. This approach generalizes to a wide collection of spaces. The authors then consider the interpolation problem in the space of bounded analytic functions on the bidisk and give a complete description of the solution. They then consider very general interpolation problems. The book includes developments of all the theory that is needed, including operator model theory, the Arveson extension theorem, and the hereditary functional calculus.