Functions of Omega-Bounded Type

Basic Theory
1. Auflage 2024
ISBN: 978-3-031-49884-8
Verlag: Birkhäuser

Buch, Englisch, 362 Seiten, Format (B × H): 168 mm x 240 mm, Gewicht: 636 g

Reihe: Frontiers in Mathematics

The book gives the basic results of the theory of the spaces A? of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ? permitting any rate of growth of a function near the boundary of the domain. This continues and essentially improves M.M. Djrbashian's theory of spaces Aa (1945) of functions holomorphic in the unit disc, the English translation of the detailed and complemented version of which (1948) is given in Addendum to the book. Besides, the book gives the ?-extensions of M. M. Djrbashian's two factorization theories of functions meromorphic in the unit disc of 1945-1948 and 1966-1975 to classes of functions delta-subharmonic in the unit disc and in the half-plane.
The book can be useful for a wide range of readers. It can be a good handbook for Master, PhD students and Postdoctoral Researchers for enlarging their knowledge and analytical methods, as well as a useful resource for scientists who want to extend their investigation fields.

Zielgruppe

Research

Autoren/Hrsg.

Jerbashian, Armen M.

Restrepo, Joel E.

Fachgebiete

• Mathematik | Informatik Mathematik Mathematische Analysis Funktionalanalysis
• Mathematik | Informatik Mathematik Mathematische Analysis Vektoranalysis, Physikalische Felder
• Mathematik | Informatik Mathematik Mathematische Analysis Funktionentheorie, Komplexe Analysis

Inhaltsverzeichnis

Introduction.- Part I Omega-Weighted Classes of Area Integrable Regular Functions. - Preliminary Results.- Spaces A(D) in the Unit Disc.- Spaces A(C) of Entire Functions. - Nevanlinna-Djrbashian Classes of Functions Delta-Subharmonic in the Unit Disc. - Spaces A?(G+) in the Halfplane.- Orthogonal Decomposition of Functions Subharmonic in the Halfplane.- Nevanlinna-Djrbashian Classes in the Halfplane.- Part II Delta-Subharmonic Extension of M.M. Djrbashian Factorization Theory.- Extension of the Factorization Theory of M.M. Djrbashian.- Banach Spaces of Functions Delta-Subharmonic in the Unit Disc.- Functions of Omega-Bounded Type in the Halfplane.- Subclasses of Harmonic Functions with Nonnegative Harmonic Majorants in the Halfplane.- Subclasses of Delta-Subharmonic Functions of Bounded Type in the Halfplane.- Banach Spaces of Functions Delta-Subharmonic in the Halfplane. - ADDENDUM.

Über Autor(innen)

Armen M. Jerbashian is a researcher at the Institute of Mathematics, National Academy of Sciences of Armenia. He is well-known to specialists by his monograph “Functions of a-Bounded Type in the Half-Plane” (Springer, 2005) and exclusive results in the field of the Nevanlinna-Djrbashian theories and related topics. He has participated in several international conferences, seminars and other related events and has been involved in the organization of some of them. His research interests are mainly in complex analysis, weighted spaces of regular functions, and operator theory.

Joel E. Restrepo is a postdoctoral researcher at the Ghent Analysis and PDE Center at Ghent University in Belgium. Previously, he was a postdoctoral researcher at different research centers in Russia and Kazakhstan. He has carried out mathematical research in a variety of topics connecting different areas of mathematics. His research links several techniques in complex analysis, operator theory, harmonic analysis, PDEs, etc. He has participated in many international conferences, seminars and other related events and has been involved in the organization of several of these scientific projects as well. In 2019, he was awarded by the International Society for Analysis, its Applications and Computation (ISSAC) with the life membership, in view of his achievements and contributions to the theory of weighted classes of delta-subharmonic functions and potential theory.