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Functions of Omega-Bounded Type: Basic Theory de Armen M. Jerbashian

Functions of Omega-Bounded Type: Basic Theory: Frontiers in Mathematics

Autor Armen M. Jerbashian, Joel E. Restrepo
en Limba Engleză Paperback – 28 feb 2024
The book gives the basic results of the theory of the spaces Apω of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ω 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 Apα (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 ω-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.
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Specificații

ISBN-13: 9783031498848
ISBN-10: 3031498844
Pagini: 360
Ilustrații: XVII, 360 p.
Dimensiuni: 168 x 240 mm
Greutate: 0.6 kg
Ediția:2024
Editura: Springer Nature Switzerland
Colecția Birkhäuser
Seria Frontiers in Mathematics

Locul publicării:Cham, Switzerland

Cuprins

- Part I Omega-Weighted Classes of Area Integrable Regular Functions. - Preliminary Results. - Spaces Apω(D) in the Unit Disc. - Spaces Apω(C) of Entire Functions. - Nevanlinna–Djrbashian Classes of Functions Delta-Subharmonic in the Unit Disc. - Spaces Apw,ᵧ(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..

Notă biografică

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.

Textul de pe ultima copertă

The book gives the basic results of the theory of the spaces Apω of functions holomorphic in the unit disc, halfplane and in the finite complex plane, which depend on functional weights ω 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 Apα (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 ω-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.

Caracteristici

Serves as a textbook for a course on the theory of functions of omega-bounded type in some domains of the complex plane Provides a self-contained complete study of the modern developments in the study of functions of omega-bounded type Provides a step-by-step guide to facts and techniques of the theory of functions of omega-bounded type