数学分析中的前沿话题(英文)

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