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The Resource Derivatives of Inner Functions, by Javad Mashreghi, (electronic resource)
Derivatives of Inner Functions, by Javad Mashreghi, (electronic resource)
Resource Information
The item Derivatives of Inner Functions, by Javad Mashreghi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item Derivatives of Inner Functions, by Javad Mashreghi, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 Derivatives of Inner Functions was inspired by a conference held at the Fields Institute in 2011 entitled "Blaschke Products and Their Applications." 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 the early twentieth century and the literature on this topic is vast. This book is devoted to a concise study of derivatives of inner functions and is confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. This selfcontained monograph allows researchers to get acquainted with the essentials of inner functions, rendering this theory accessible to graduate students while providing the reader with rapid access to the frontiers of research in this field
 Language

 eng
 eng
 Edition
 1st ed. 2013.
 Extent
 1 online resource (175 p.)
 Note
 Description based upon print version of record
 Contents

 Derivatives of Inner Functions; Preface; Contents; Chapter 1: Inner Functions; 1.1 The Poisson Integral of a Measure; 1.2 The Hardy Space Hp(D); 1.3 Two Classes of Inner Functions; 1.4 The Canonical Factorization; 1.5 A Characterization of Blaschke Products; 1.6 The Nevanlinna Class N and Its Subclass N+; 1.7 Bergman Spaces; Chapter 2: The Exceptional Set of an Inner Function; 2.1 Frostman Shifts and the Exceptional Set ε; 2.2 Capacity; 2.3 Hausdorff Dimension; 2.4 ε Has Logarithmic Capacity Zero; 2.5 The Cluster Set at a Boundary Point; Chapter 3: The Derivative of Finite Blaschke Products
 3.1 Elementary Formulas for B'3.2 The Cardinality of the Zeros of B'; 3.3 A Formula for B'; 3.4 The Locus of the Zeros of B' in D; 3.5 B Has a Nonzero Residue; Chapter 4: Angular Derivative; 4.1 Elementary Formulas for B' and S'; 4.2 Some Estimations for HpMeans; 4.3 Some Estimations for ApMeans; 4.4 The Angular Derivative; 4.5 The Carathéodory Derivative; 4.6 Another Characterization of the Carathéodory Derivative; Chapter 5: HpMeans of S'; 5.1 The Effect of Singular Factors; 5.2 A Characterization of Φ' Hp(D); 5.3 We Never Have S' H12(D); 5.4 The Distance Function
 10.2 HpMeans of the First Derivative10.3 HpMeans of Higher Derivatives; 10.4 ApMeans of the First Derivative; References; Index
 Isbn
 9781283909808
 Label
 Derivatives of Inner Functions
 Title
 Derivatives of Inner Functions
 Statement of responsibility
 by Javad Mashreghi
 Language

 eng
 eng
 Summary
 Derivatives of Inner Functions was inspired by a conference held at the Fields Institute in 2011 entitled "Blaschke Products and Their Applications." 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 the early twentieth century and the literature on this topic is vast. This book is devoted to a concise study of derivatives of inner functions and is confined to treating the integral means of derivatives and presenting a comprehensive list of results on Hardy and Bergman means. This selfcontained monograph allows researchers to get acquainted with the essentials of inner functions, rendering this theory accessible to graduate students while providing the reader with rapid access to the frontiers of research in this field
 http://library.link/vocab/creatorName
 Mashreghi, Javad
 Dewey number
 620.1
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 mmOXdVkXv_k
 Language note
 English
 LC call number
 QA331355
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Fields Institute Monographs,
 Series volume
 31
 http://library.link/vocab/subjectName

 Functions of complex variables
 Functional analysis
 Differential equations, partial
 Functions of a Complex Variable
 Functional Analysis
 Several Complex Variables and Analytic Spaces
 Label
 Derivatives of Inner Functions, by Javad Mashreghi, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Derivatives of Inner Functions; Preface; Contents; Chapter 1: Inner Functions; 1.1 The Poisson Integral of a Measure; 1.2 The Hardy Space Hp(D); 1.3 Two Classes of Inner Functions; 1.4 The Canonical Factorization; 1.5 A Characterization of Blaschke Products; 1.6 The Nevanlinna Class N and Its Subclass N+; 1.7 Bergman Spaces; Chapter 2: The Exceptional Set of an Inner Function; 2.1 Frostman Shifts and the Exceptional Set ε; 2.2 Capacity; 2.3 Hausdorff Dimension; 2.4 ε Has Logarithmic Capacity Zero; 2.5 The Cluster Set at a Boundary Point; Chapter 3: The Derivative of Finite Blaschke Products
 3.1 Elementary Formulas for B'3.2 The Cardinality of the Zeros of B'; 3.3 A Formula for B'; 3.4 The Locus of the Zeros of B' in D; 3.5 B Has a Nonzero Residue; Chapter 4: Angular Derivative; 4.1 Elementary Formulas for B' and S'; 4.2 Some Estimations for HpMeans; 4.3 Some Estimations for ApMeans; 4.4 The Angular Derivative; 4.5 The Carathéodory Derivative; 4.6 Another Characterization of the Carathéodory Derivative; Chapter 5: HpMeans of S'; 5.1 The Effect of Singular Factors; 5.2 A Characterization of Φ' Hp(D); 5.3 We Never Have S' H12(D); 5.4 The Distance Function
 10.2 HpMeans of the First Derivative10.3 HpMeans of Higher Derivatives; 10.4 ApMeans of the First Derivative; References; Index
 Dimensions
 unknown
 Edition
 1st ed. 2013.
 Extent
 1 online resource (175 p.)
 Form of item
 online
 Isbn
 9781283909808
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461456117
 Specific material designation
 remote
 System control number

 (CKB)2670000000279092
 (EBL)1081961
 (OCoLC)821031019
 (SSID)ssj0000798521
 (PQKBManifestationID)11510594
 (PQKBTitleCode)TC0000798521
 (PQKBWorkID)10743908
 (PQKB)11788166
 (DEHe213)9781461456117
 (MiAaPQ)EBC1081961
 (EXLCZ)992670000000279092
 Label
 Derivatives of Inner Functions, by Javad Mashreghi, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents

 Derivatives of Inner Functions; Preface; Contents; Chapter 1: Inner Functions; 1.1 The Poisson Integral of a Measure; 1.2 The Hardy Space Hp(D); 1.3 Two Classes of Inner Functions; 1.4 The Canonical Factorization; 1.5 A Characterization of Blaschke Products; 1.6 The Nevanlinna Class N and Its Subclass N+; 1.7 Bergman Spaces; Chapter 2: The Exceptional Set of an Inner Function; 2.1 Frostman Shifts and the Exceptional Set ε; 2.2 Capacity; 2.3 Hausdorff Dimension; 2.4 ε Has Logarithmic Capacity Zero; 2.5 The Cluster Set at a Boundary Point; Chapter 3: The Derivative of Finite Blaschke Products
 3.1 Elementary Formulas for B'3.2 The Cardinality of the Zeros of B'; 3.3 A Formula for B'; 3.4 The Locus of the Zeros of B' in D; 3.5 B Has a Nonzero Residue; Chapter 4: Angular Derivative; 4.1 Elementary Formulas for B' and S'; 4.2 Some Estimations for HpMeans; 4.3 Some Estimations for ApMeans; 4.4 The Angular Derivative; 4.5 The Carathéodory Derivative; 4.6 Another Characterization of the Carathéodory Derivative; Chapter 5: HpMeans of S'; 5.1 The Effect of Singular Factors; 5.2 A Characterization of Φ' Hp(D); 5.3 We Never Have S' H12(D); 5.4 The Distance Function
 10.2 HpMeans of the First Derivative10.3 HpMeans of Higher Derivatives; 10.4 ApMeans of the First Derivative; References; Index
 Dimensions
 unknown
 Edition
 1st ed. 2013.
 Extent
 1 online resource (175 p.)
 Form of item
 online
 Isbn
 9781283909808
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9781461456117
 Specific material designation
 remote
 System control number

 (CKB)2670000000279092
 (EBL)1081961
 (OCoLC)821031019
 (SSID)ssj0000798521
 (PQKBManifestationID)11510594
 (PQKBTitleCode)TC0000798521
 (PQKBWorkID)10743908
 (PQKB)11788166
 (DEHe213)9781461456117
 (MiAaPQ)EBC1081961
 (EXLCZ)992670000000279092
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