数学分析中的前沿话题(英文)
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作者编者:(英)迈克尔·鲁然斯基//(印)希曼·杜塔|责编:聂兆慈//李兰静
出版社哈尔滨工业大学
ISBN9787576710007
出版时间2024-01
装帧其他
开本其他
定价198元
货号1203222553
上书时间2024-06-12
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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
内容摘要
本书共有17章，具体内容包含无限维动力学中的随机测度、利用矩阵方法的若干矩阵不等式的扩展、仿射群上的函数方程、局部伪凸空间与代数、奇异积分算子与交换子的应用、经典不等式应用的复合子测度和超测度、广义二重统计加权可和性及其科洛夫金、近似定理、伯克霍夫－詹姆斯、正交性及其在研究巴拿赫空间几何性质中的应用、具有图形结构的度量空间上映射的不动点等。本书的目标读者是对数学，特别是对数学分析感兴趣的研究者、研究生和教育者。本书旨在展示理论、方法和章节中所选主题的应用。
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