Derivatives Of Inner Functions
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Derivatives Of Inner Functions
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Author : Javad Mashreghi
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-11-14
Derivatives Of Inner Functions written by Javad Mashreghi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-14 with Mathematics categories.
Inner functions form an important subclass of bounded analytic functions. Since they have unimodular boundary values, they appear in many extremal problems of complex analysis. They have been extensively studied since early last century, and the literature on this topic is vast. Therefore, this book is devoted to a concise study of derivatives of these objects, and confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. The goal is to provide rapid access to the frontiers of research in this field. This monograph will allow researchers to get acquainted with essentials on inner functions, and it is self-contained, which makes it accessible to graduate students.
Derivatives Of Inner Functions
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Author : Hong Oh Kim
language : en
Publisher:
Release Date : 1982
Derivatives Of Inner Functions written by Hong Oh Kim and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Holomorphic functions categories.
Norm Derivatives And Characterizations Of Inner Product Spaces
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Author : Claudi Alsina
language : en
Publisher: World Scientific
Release Date : 2010
Norm Derivatives And Characterizations Of Inner Product Spaces written by Claudi Alsina and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010 with Mathematics categories.
1. Introduction. 1.1. Historical notes. 1.2. Normed linear spaces. 1.3. Strictly convex normed linear spaces. 1.4. Inner product spaces. 1.5. Orthogonalities in normed linear spaces -- 2. Norm derivatives. 2.1. Norm derivatives : Definition and basic properties. 2.2. Orthogonality relations based on norm derivatives. 2.3. p'[symbol]-orthogonal transformations. 2.4. On the equivalence of two norm derivatives. 2.5. Norm derivatives and projections in normed linear spaces. 2.6. Norm derivatives and Lagrange's identity in normed linear spaces. 2.7. On some extensions of the norm derivatives. 2.8. p-orthogonal additivity -- 3. Norm derivatives and heights. 3.1. Definition and basic properties. 3.2. Characterizations of inner product spaces involving geometrical properties of a height in a triangle. 3.3. Height functions and classical orthogonalities. 3.4. A new orthogonality relation. 3.5. Orthocenters. 3.6. A characterization of inner product spaces involving an isosceles trapezoid property. 3.7. Functional equations of the height transform -- 4. Perpendicular bisectors in Normed spaces. 4.1. Definitions and basic properties. 4.2. A new orthogonality relation. 4.3. Relations between perpendicular bisectors and classical orthogonalities. 4.4. On the radius of the circumscribed circumference of a triangle. 4.5. Circumcenters in a triangle. 4.6. Euler line in real normed space. 4.7. Functional equation of the perpendicular bisector transform -- 5. Bisectrices in real Normed spaces. 5.1. Bisectrices in real normed spaces. 5.2. A new orthogonality relation. 5.3. Functional equation of the bisectrix transform. 5.4. Generalized bisectrices in strictly convex real normed spaces. 5.5. Incenters and generalized bisectrices -- 6. Areas of triangles in Normed spaces. 6.1. Definition of four areas of triangles. 6.2. Classical properties of the areas and characterizations of inner product spaces. 6.3. Equalities between different area functions. 6.4. The area orthogonality.
Complex Analysis And Potential Theory
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Author : Andre Boivin
language : en
Publisher: American Mathematical Soc.
Release Date : 2012
Complex Analysis And Potential Theory written by Andre Boivin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.
This is the proceedings volume of an international conference entitled Complex Analysis and Potential Theory, which was held to honor the important contributions of two influential analysts, Kohur N. GowriSankaran and Paul M. Gauthier, in June 2011 at the Centre de Recherches Mathematiques (CRM) in Montreal. More than fifty mathematicians from fifteen countries participated in the conference. The twenty-four surveys and research articles contained in this book are based on the lectures given by some of the most established specialists in the fields. They reflect the wide breadth of research interests of the two honorees: from potential theory on trees to approximation on Riemann surfaces, from universality to inner and outer functions and the disc algebra, from branching processes to harmonic extension and capacities, from harmonic mappings and the Harnack principle to integration formulae in $\mathbb {C}^n$ and the Hartogs phenomenon, from fine harmonicity and plurisubharmonic functions to the binomial identity and the Riemann hypothesis, and more. This volume will be a valuable resource for specialists, young researchers, and graduate students from both fields, complex analysis and potential theory. It will foster further cooperation and the exchange of ideas and techniques to find new research perspectives.
The Dirichlet Space And Related Function Spaces
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Author : Nicola Arcozzi
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-09-03
The Dirichlet Space And Related Function Spaces written by Nicola Arcozzi and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-09-03 with Mathematics categories.
The study of the classical Dirichlet space is one of the central topics on the intersection of the theory of holomorphic functions and functional analysis. It was introduced about100 years ago and continues to be an area of active current research. The theory is related to such important themes as multipliers, reproducing kernels, and Besov spaces, among others. The authors present the theory of the Dirichlet space and related spaces starting with classical results and including some quite recent achievements like Dirichlet-type spaces of functions in several complex variables and the corona problem. The first part of this book is an introduction to the function theory and operator theory of the classical Dirichlet space, a space of holomorphic functions on the unit disk defined by a smoothness criterion. The Dirichlet space is also a Hilbert space with a reproducing kernel, and is the model for the dyadic Dirichlet space, a sequence space defined on the dyadic tree. These various viewpoints are used to study a range of topics including the Pick property, multipliers, Carleson measures, boundary values, zero sets, interpolating sequences, the local Dirichlet integral, shift invariant subspaces, and Hankel forms. Recurring themes include analogies, sometimes weak and sometimes strong, with the classical Hardy space; and the analogy with the dyadic Dirichlet space. The final chapters of the book focus on Besov spaces of holomorphic functions on the complex unit ball, a class of Banach spaces generalizing the Dirichlet space. Additional techniques are developed to work with the nonisotropic complex geometry, including a useful invariant definition of local oscillation and a sophisticated variation on the dyadic Dirichlet space. Descriptions are obtained of multipliers, Carleson measures, interpolating sequences, and multiplier interpolating sequences; estimates are obtained to prove corona theorems.
Differentiation Of Real Functions
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Author : A. M. Bruckner
language : en
Publisher: Springer
Release Date : 2006-11-15
Differentiation Of Real Functions written by A. M. Bruckner and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
Active Calculus 2018
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Author : Matthew Boelkins
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-08-13
Active Calculus 2018 written by Matthew Boelkins and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-13 with categories.
Active Calculus - single variable is a free, open-source calculus text that is designed to support an active learning approach in the standard first two semesters of calculus, including approximately 200 activities and 500 exercises. In the HTML version, more than 250 of the exercises are available as interactive WeBWorK exercises; students will love that the online version even looks great on a smart phone. Each section of Active Calculus has at least 4 in-class activities to engage students in active learning. Normally, each section has a brief introduction together with a preview activity, followed by a mix of exposition and several more activities. Each section concludes with a short summary and exercises; the non-WeBWorK exercises are typically involved and challenging. More information on the goals and structure of the text can be found in the preface.
Introduction To Model Spaces And Their Operators
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Author : Stephan Ramon Garcia
language : en
Publisher: Cambridge University Press
Release Date : 2016-05-17
Introduction To Model Spaces And Their Operators written by Stephan Ramon Garcia and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-05-17 with Mathematics categories.
A self-contained textbook which opens up this challenging field to newcomers and points to areas of future research.
Calculus And Ordinary Differential Equations
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Author : Dr. Navneet Kumar Lamba
language : en
Publisher: RK Publication
Release Date : 2024-10-17
Calculus And Ordinary Differential Equations written by Dr. Navneet Kumar Lamba and has been published by RK Publication this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-10-17 with Mathematics categories.
Calculus and Ordinary Differential Equations a comprehensive introduction to two fundamental areas of mathematics: calculus and ordinary differential equations (ODEs). The explores core concepts of differentiation, integration, and limits, alongside the theory and methods for solving first-order and higher-order differential equations. Through a blend of theory, examples, and applications, it aims to equip readers with essential mathematical tools for analyzing dynamic systems, modeling real-world phenomena, and understanding the mathematical foundations of science and engineering.
A Mathematics Course For Political And Social Research
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Author : Will H. Moore
language : en
Publisher: Princeton University Press
Release Date : 2013-07-24
A Mathematics Course For Political And Social Research written by Will H. Moore and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07-24 with Political Science categories.
Political science and sociology increasingly rely on mathematical modeling and sophisticated data analysis, and many graduate programs in these fields now require students to take a "math camp" or a semester-long or yearlong course to acquire the necessary skills. Available textbooks are written for mathematics or economics majors, and fail to convey to students of political science and sociology the reasons for learning often-abstract mathematical concepts. A Mathematics Course for Political and Social Research fills this gap, providing both a primer for math novices in the social sciences and a handy reference for seasoned researchers. The book begins with the fundamental building blocks of mathematics and basic algebra, then goes on to cover essential subjects such as calculus in one and more than one variable, including optimization, constrained optimization, and implicit functions; linear algebra, including Markov chains and eigenvectors; and probability. It describes the intermediate steps most other textbooks leave out, features numerous exercises throughout, and grounds all concepts by illustrating their use and importance in political science and sociology. Uniquely designed and ideal for students and researchers in political science and sociology Uses practical examples from political science and sociology Features "Why Do I Care?" sections that explain why concepts are useful Includes numerous exercises Complete online solutions manual (available only to professors, email david.siegel at duke.edu, subject line "Solution Set") Selected solutions available online to students