作者：【英】迈克尔·鲁然斯基
页数：594
出版社：哈尔滨工业大学出版社
出版日期：2024
ISBN：9787576710007
电子书格式：pdf/epub/txt
内容简介
本书是一部英文的数学分析专著，中文书名可译为《数学分析中的前言话题》，本书的主编有两位，一位是迈克尔.鲁然斯基（Michael Ruzhansky），英国人，帝国理工大学数学系教授，另一位是希曼.杜塔（Hemen Dutta），印度人，印度高哈蒂大学数学系助教。
目录
Preface
Contributors
1 Random Measures in Infinite-Dimensional Dynamics
Palle E.T. Jorgcnsen and Feng Tian
1.1 Introduction, history, and motivation
1.2 R.KHSs in measurable category: new settings for positivity conditions
1.3 L2loc(λ) vs L2(A): Local versus global L2-conditions
1.4 Continuous networks: Atomic versus non-atomic models
1.5 New correspondences
A. 1 Applications of RKHSs: An overview
A.2 Duality of representations, and some of their applications
2 Extensions of Some Matrix Inequalities via Matrix Means Takeaki Yamazaki
2.1 Matrix monotone function
2.2 Matrix means
2.3 Matrix power mean
2.4 Karcher mean
3 Functional Equations on Affine Groups
Laszlo Szdkelyhidi
3.1 Introduction
3.2 Semidirect products
3.3 Linear groups
3.4 Affine groups
3.5 Invariant functions and measures
3.6 Spherical functions and functional equations
3.7 Functional equations on Euclidean motion groups
3.8 Afline groups of generalized orthogonal groups
4 Locally Pseudoconvex Spaces and Algebras Mati Abel
4.1 Brief introduction
4.1.1 Linear spaces
4.1.2 Topological spaces
4.2 Topological linear spaces
4.2.1 Topological algebras
4.3 Topology of a linear space and an algebra, defined by a collection of F-seminorms
4.4 Locally pseudoconvex spaces and algebras
4.4.1 Saturation of a collection of seminorms
4.5 Locally bounded space and algebra
4.6 Main types of locally pseudoconvex algebras
4.7 Generalizations of Gelfand-Mazur theorem for locally pseudoconvex division algebras
4.8 Generalizations of Arens-Michael theorem for locally pseudoconvex algebras
4.9 Generalization of Akkar teorem for locally pseudoconvex algebras
5 Applications of Singular Integral Operators and Commutators
Andrea Scapellato
5.1 Introduction
5.2 BMO class
5.3 VMO class
5.4 Morrey-Campanato spaces
5.5 Generalized Morrey spaces
5.6 Mixed Morrey spaces
5.7 Applications to partial differential equations
5.7.1 Elliptic equations
5.7.1.1 Preliminary tools
5.7.1.2 Nondivergence form elliptic equations
5.7.1.3 Representation formula
5.7.1.4 Regularity
5.7.1.5 Divergence form elliptic equations
5.7.2 Parabolic equations
5.7.2.1 Preliminary tools
5.7.2.2 Nondivergence form parabolic equations
5.7.2.3 Divergence form parabolic equations
5.7.3 Ultraparabolic equations
5.7.3.1 Preliminary tools
5.7.3.2 Nondivergence form ultraparabolic equations
5.7.3.3 Divergence form ultraparabolic equations
……
6 Composite Submeasures and Supermeasures with Applica-
tions to Classical Inequalities
7 Generalized Double Statistical Weighted Summability and
Its Application to Korovkin Type Approximation Theorem
8 Birkhoff-James orthogonality and Its Application in the
Study of Geometry of Banach Space
9 Fixed Point of Mappings on Metric Space Endowed with
Graphic Structure
10 Some Subclasses of Analytic Unctions and Their Properties
11 Free Stochastic Integrals for Weighted—Semicircular Motion
Induced by Orthogonal Projections
12 On Difference Operators and Their Applications
13 Composite Ostrowski and Trapezoid Type Inequalities for
Riemann-Liouville Fractional Integrals of Functions with
Bounded Variation
14 kn-2 Scalar Matrix and Its Functional Equations by
Mathematical Modeling
15 Renorming Co and Fixed Point Property
16 Steinhaus Type Theorems over Valued Fields：A Survey
17 The Interplay Between Topological Algebras Theory and
Algebras of Holomorphic Functions
Contributors
1 Random Measures in Infinite-Dimensional Dynamics
Palle E.T. Jorgcnsen and Feng Tian
1.1 Introduction, history, and motivation
1.2 R.KHSs in measurable category: new settings for positivity conditions
1.3 L2loc(λ) vs L2(A): Local versus global L2-conditions
1.4 Continuous networks: Atomic versus non-atomic models
1.5 New correspondences
A. 1 Applications of RKHSs: An overview
A.2 Duality of representations, and some of their applications
2 Extensions of Some Matrix Inequalities via Matrix Means Takeaki Yamazaki
2.1 Matrix monotone function
2.2 Matrix means
2.3 Matrix power mean
2.4 Karcher mean
3 Functional Equations on Affine Groups
Laszlo Szdkelyhidi
3.1 Introduction
3.2 Semidirect products
3.3 Linear groups
3.4 Affine groups
3.5 Invariant functions and measures
3.6 Spherical functions and functional equations
3.7 Functional equations on Euclidean motion groups
3.8 Afline groups of generalized orthogonal groups
4 Locally Pseudoconvex Spaces and Algebras Mati Abel
4.1 Brief introduction
4.1.1 Linear spaces
4.1.2 Topological spaces
4.2 Topological linear spaces
4.2.1 Topological algebras
4.3 Topology of a linear space and an algebra, defined by a collection of F-seminorms
4.4 Locally pseudoconvex spaces and algebras
4.4.1 Saturation of a collection of seminorms
4.5 Locally bounded space and algebra
4.6 Main types of locally pseudoconvex algebras
4.7 Generalizations of Gelfand-Mazur theorem for locally pseudoconvex division algebras
4.8 Generalizations of Arens-Michael theorem for locally pseudoconvex algebras
4.9 Generalization of Akkar teorem for locally pseudoconvex algebras
5 Applications of Singular Integral Operators and Commutators
Andrea Scapellato
5.1 Introduction
5.2 BMO class
5.3 VMO class
5.4 Morrey-Campanato spaces
5.5 Generalized Morrey spaces
5.6 Mixed Morrey spaces
5.7 Applications to partial differential equations
5.7.1 Elliptic equations
5.7.1.1 Preliminary tools
5.7.1.2 Nondivergence form elliptic equations
5.7.1.3 Representation formula
5.7.1.4 Regularity
5.7.1.5 Divergence form elliptic equations
5.7.2 Parabolic equations
5.7.2.1 Preliminary tools
5.7.2.2 Nondivergence form parabolic equations
5.7.2.3 Divergence form parabolic equations
5.7.3 Ultraparabolic equations
5.7.3.1 Preliminary tools
5.7.3.2 Nondivergence form ultraparabolic equations
5.7.3.3 Divergence form ultraparabolic equations
……
6 Composite Submeasures and Supermeasures with Applica-
tions to Classical Inequalities
7 Generalized Double Statistical Weighted Summability and
Its Application to Korovkin Type Approximation Theorem
8 Birkhoff-James orthogonality and Its Application in the
Study of Geometry of Banach Space
9 Fixed Point of Mappings on Metric Space Endowed with
Graphic Structure
10 Some Subclasses of Analytic Unctions and Their Properties
11 Free Stochastic Integrals for Weighted—Semicircular Motion
Induced by Orthogonal Projections
12 On Difference Operators and Their Applications
13 Composite Ostrowski and Trapezoid Type Inequalities for
Riemann-Liouville Fractional Integrals of Functions with
Bounded Variation
14 kn-2 Scalar Matrix and Its Functional Equations by
Mathematical Modeling
15 Renorming Co and Fixed Point Property
16 Steinhaus Type Theorems over Valued Fields：A Survey
17 The Interplay Between Topological Algebras Theory and
Algebras of Holomorphic Functions
