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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Extensions of Projection Theorem in Banach Spaces
投影定理 巴拿赫空间 扩展
2023/5/4
In this talk, we first recall classic projection theorem for closed convex subsets in a Hilbert space. Then we introduce two extensions of the projection theorem in the Banach space where one is estab...
Banach space theory is the main theme of this proposal. This theory has a long history going back to the pioneering works by Stefan Banach in the 1930s. It is well-known nowadays that Banach space the...
EMBEDDINGS OF SOME CLASSICAL BANACH SPACES INTO MODULATION SPACES
Besov space modulation space Sobolev space short-time Fourier transform Triebel-Lizorkin space time-frequency analysis
2015/12/10
We give sufficient conditions for a tempered distribution to belong to certain modulation spaces by showing embeddings of some Besov-TriebelLizorkin spaces into modulation spaces. As aconsequence we h...
The Maslov index in symplectic Banach spaces.
Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces
Fixed Point Various Iterative Schemes Rate of Convergence
2013/1/30
In this paper, we suggest a new type of three step iterative scheme called the CR iterative scheme and study the strong convergence of this iterative scheme for a certain class of quasi-contractive op...
Solving Support Vector Machines in Reproducing Kernel Banach Spaces with Positive Definite Functions
support vector machine reproducing kernel Banach space reproducing kernel,posi-tive definite function Fourier transform,Sobolev space,Matern function,Sobolev spline
2012/11/22
In this paper we extend support vector machines from reproducing kernel Hilbert spaces into reproducing kernel Banach spaces whose reproducing kernels can be defined on nonsymmetric domains. Using the...
Strictly stationary solutions of ARMA equations in Banach spaces
Strictly stationary solutions ARMA equations Banach spaces Probability
2012/6/21
We obtain necessary and sufficient conditions for the existence of strictly stationary solutions of ARMA equations in Banach spaces with independent and identically distributed noise under certain ass...
On removability properties of $ψ$-uniform domains in Banach spaces
Uniform domain uniform domain removability property quasihyperbolic metric
2012/6/9
Suppose that $E$ and $E'$ denote real Banach spaces with the same dimension at least 2. The main aim of this paper is to show that a domain $D$ in $E$ is a $\psi$-uniform domain if and only if $D\back...
Tools for Malliavin calculus in UMD Banach spaces
Malliavin calculus Skorohod integral anticipating processes Meyer inequalities UMD Banach space type 2 space chain rule
2012/4/16
In this paper we study the Malliavin derivatives and Skorohod integrals for processes taking values in an infinite dimensional space. Such results are motivated by their applications to SPDEs and in p...
Reflexive Operator Algebras on Banach Spaces
operator algebras invariant subspace lattice Boolean algebra of projections spectral operator
2012/4/18
In this paper we study the reflexivity of a unital strongly closed algebra of operators with complemented invariant subspace lattice on a Banach space. We prove that if such an algebra contains a comp...
Fixed Points Theorems of Ordered Contractive Maps on Noncommutative Banach spaces
Fixed point Order contractive map Noncommutative Banach space
2011/10/26
The paper introduces the concept of noncommutative Banach spaces and obtains several fixed point theorems for continuous or discontinuous ordered contractive maps in ordered noncommutative Banach spac...
Characterization of uniformly convex and smooth Banach spaces by using Carleson measures in Bessel settings
BMO Bessel operators Carleson measures uniformly convex uniformly smooth Banach spaces
2011/9/22
Abstract: In this paper we obtain new characterizations of the q-uniformly convex and smooth Banach spaces by using Carleson measures. These measures are defined by Poisson integral associated with Be...
Variational Inequalities and Improved Convergence Rates for Tikhonov Regularisation on Banach Spaces
Variational Inequalities Improved Convergence Rates Tikhonov Regularisation Optimization and Control
2011/9/5
Abstract: In this paper we derive higher order convergence rates in terms of the Bregman distance for Tikhonov like convex regularisation for linear operator equations on Banach spaces. The approach i...
Poincare inequalities and rigidity for actions on Banach spaces
Poincare inequality Kazhdan’s property (T) affine isometric action
2011/8/31
Abstract: The aim of this paper is to extend the framework of the spectral method for proving property (T) to the class of reflexive Banach spaces and present conditions implying that every affine iso...
Radon-Nikodým compact spaces of low weight and Banach spaces
Radon-Nikod´ ym compact quasi Radon-Nikod´ ym compact
2011/2/28
We prove that a continuous image of a Radon-Nikod´ym compact of weight less than b is Radon-Nikod´ym compact. As a Banach space counter-part, subspaces of Asplund generated Banach spaces o...