Boundedness for some Schrödinger type operators on Morrey spaces related to certain nonnegative potentials

In this paper, we establish the boundedness of some Schrödinger type operators on Morrey spaces related to certain nonnegative potentials belonging to the reverse Hölder class.     

Hankel operators in the set of essential Toeplitz operators

In this paper, we study the Hankel operators belonging toE which denotes all of the essential Toeplitz operators, and show that the class of symbols of these Hankel operators is a Douglas algebra. Meanwhile, using the concept of essential commutant and some knowledge of the theory of function algebras, we solve a problem raised by Josè Barria and P. R. Halmos in [1].     

Classification of block-toeplitz h-normal operators

In our previous paper [2] a special class of normal operators acting in spaces with indefinite scalar product was introduced. The operators from this class are characterized by the property that in appropriate sip orthogonal bases their matrices have diagonal block-Toeplitz forms. In the present paper we find a complete system of invariants and canonical form for operators belonging to this class.     

Classification of block-toeplitz h-normal operators

In our previous paper [2] a special class of normal operators acting in spaces with indefinite scalar product was introduced. The operators from this class are characterized by the property that in appropriate sip orthogonal bases their matrices have diagonal block-Toeplitz forms. In the present paper we find a complete system of invariants and canonical form for operators belonging to this class.     

由具奇异系数的强椭圆微分算子生成的解析半群

本文提出了低阶项系数具一定奇异性的高阶强椭圆微分算子生成解析半群的条 件,其包含了低阶项系数属于Schecter位势类的情形.特别地,低阶项系数属于LP(Rn) 的情形也在其中.作为应用,得到低阶项系数属于LP(Rn)的强椭圆算子的相应半群生 成,且p还可取到一些临界值.     

A viscosity method with no spectral radius requirements for the split common fixed point problem

This paper is concerned with an algorithmic solution to the split common fixed point problem in Hilbert spaces. Our method can be regarded as a variant of the “viscosity approximation method”. Under very classical assumptions, we establish a strong convergence theorem with regard to involved operators belonging to the wide class of quasi-nonexpansive operators. In contrast with other related processes, our algorithm does not require any estimate of some spectral radius. The technique of analysis developed in this work is new and can be applied to many other fixed point iterations. Numerical experiments are also performed with regard to an inverse heat problem.     

Pseudodifferential Operators Associated with a Semigroup of Operators

Related to a semigroup of operators on a metric measure space, we define and study pseudodifferential operators (including the setting of Riemannian manifolds, fractals, graphs etc.). Boundedness on L ^p for pseudodifferential operators of order 0 is proved. We mainly focus on symbols belonging to the class $S^{0}_{1,\delta}$ for δ∈[0,1). For the limit class $S^{0}_{1,1}$ , we describe some results by restricting our attention to the case of a sub-Laplacian operator on a Riemannian manifold.     

由Schrdinger算子定义的Riesz变换的L~p估计(英文)

本文主要讨论了当非负位势 V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x))+V(x)所定义的 Riesz变换在 L~p空间的有界性。     

由schr(o)dinger算子定义的Riesz变换的Lp估计

本文主要讨论了当非负位势V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x)(△))+V(x)所定义的Riesz变换在Lp空间的有界性.     

Équations faiblement hyperboliques du deuxième ordre et classes de fonctions ultradifférentiables

We consider a second order weakly hyperbolic equation and we study in which classes the corresponding Cauchy problem is well posed. We consider operators with coefficients depending only on the t variable and belonging to a class X between C^∞ and the real analytic class. We find then a class, strictly related to X, where the Cauchy problem is well posed. Finally, we prove by some counterexamples that these results are almost optimal.     

The Properties of Functions and Approximation by Summation Rational Operators on the Real Axis

In the space $C(\mathbb{R})$ , we construct special summation operators of Jackson type with rational kernels and under a suitable choice of poles we obtain order estimates for deviations of these operators from functions belonging to certain classes.     

Traces of operators with a relatively compact perturbation

This is a continuation of the authors’ series of papers on the theory of regularized traces of abstract discrete operators. We prove a theorem in which the perturbing operator B is subordinate to the operator A ₀ in the sense that BA ₀ ^?δ is a compact operator belonging to some Schatten-von Neumann class of finite order. Apart from covering new classes of operators, and in contrast to our preceding papers, we give a unified statement of the theorem regardless of whether the resolvent of the unperturbed operator belongs to the trace class. Two examples are given in which the result is applied to ordinary differential operators as well as to partial differential operators.     

Localized Frames and Compactness

We introduce the concept of weak localization for continuous frames and use this concept to define a class of weakly localized operators. This class contains many important classes of operators, including: short time Fourier transform multipliers, Calderon–Toeplitz operators, Toeplitz operators on various functions spaces, Anti-Wick operators, some pseudodifferential operators, some Calderon–Zygmund operators, and many others. In this paper, we study the boundedness and compactness of weakly localized operators. In particular, we provide a characterization of compactness for weakly localized operators in terms of the behavior of their Berezin transforms.     

由Schr?dinger算子定义的Riesz变换的Lp估计

本文主要讨论了当非负位势 V(x)属于某逆Holder类时,由一致椭圆算子L=-div(A(x))+V(x)所定义的 Riesz变换在 L^p空间的有界性。     

单边算子有界性和KdV型色散方程的适定性研究

数学和物理中许多重要问题均可归结为算子在某些函数空间中的有界性质.奇异积分算子有界性质的研究是调和分析理论的核心课题之一,由此发展起来的各种方法和技巧已广泛应用于偏微分方程的研究.借助奇异积分算子在Lebesgue空间或Morrey型空间中建立的时空估计和半群理论,可以得到非线性色散方程在低阶Sobolev空间中Cauchy问题的适定性.本文首次定义一类单边振荡奇异积分算子并研究该类算子的经典加权有界性质.受经典交换子刻画理论的启发,本文首次引入Morrey空间的交换子刻画理论.利用不同于常规极大函数的方法得到两类象征函数在Morrey空间中的交换子刻画.以上结果为偏微分方程的研究提供了新的工具.最后,结合能量方法和数论知识,本文解决几类KdV型色散方程的适定性问题.     

A NOTE ON MAJORIZING AND CONE ABSOLUTELY SUMMING OPERATORS IN BANACH LATTICES

Abstract

Operators T which are both majorizing and cone absolutely summing on a Banach lattice E are investigated. Compactness and nuclearity of such operators are discussed and it is shown that a trace can be defined for operators belonging to a large class of these operators. Special results are derived in the case where E is a Banach function space and T a kernel operator. Finally we derive strongly measurable representations for a certain class of cone absolutely summing operators thereby clarifying work done by Dinculeanu and J.J. Uhl.     

On the class of disjoint limited completely continuous operators

We introduce and study new class of sets (almost L-limited sets). Also, we introduce new concept of property in Banach lattice (almost Gelfand–Phillips property) and we characterize this property using almost L-limited sets. On the other hand, we introduce the class of disjoint limited completely continuous operators which is a largest class than that of limited completely continuous operators, we characterize this class of operators and we study some of its properties.     

Spectral properties of a class of reflectionless Schrödinger operators

We prove that one-dimensional reflectionless Schrödinger operators with spectrum a homogeneous set in the sense of Carleson, belonging to the class introduced by Sodin and Yuditskii, have purely absolutely continuous spectra. This class includes all earlier examples of reflectionless almost periodic Schrödinger operators. In addition, we construct examples of reflectionless Schrödinger operators with more general types of spectra, given by the complement of a Denjoy-Widom-type domain in C, which exhibit a singular component.     

Approximation Properties of a Special Class of Mathematical Expectation Operators

61-IntroductionLet(X.}"cNbeasequenceofindependentrandomvariableseachhavingthesamelatticepointdistributionwithprobabilityfunctionP(X,=a kh)=P*,expectationEX"=),l(x)andvarianceE(X"-ax")'=a2(x).WhereKeZ:={o,tl,l2,..'},a,harethepositivecon-stants,xeI=Y'=Ri8arealcontinuousparameter.LettheprobabilitydistributionofS,=ZX,beForacontinuousfunctionfontheinterval7'(possiblyinfinite)definethemathematicalex-pectationoperatorRemarks(l)UsingChebychev,sinequalitywegeteasily.(See[1,P,,,f,,.j)-(2)Manyo…     

Symbolic Computation with Monotone Operators

We consider a class of monotone operators which are appropriate for symbolic representation and manipulation within a computer algebra system. Various structural properties of the class (e.g., closure under taking inverses, resolvents) are investigated as well as the role played by maximal monotonicity within the class. In particular, we show that there is a natural correspondence between our class of monotone operators and the subdifferentials of convex functions belonging to a class of convex functions deemed suitable for symbolic computation of Fenchel conjugates which were previously studied by Bauschke & von Mohrenschildt and by Borwein & Hamilton. A number of illustrative examples utilizing the introduced class of operators are provided including computation of proximity operators, recovery of a convex penalty function associated with the hard thresholding operator, and computation of superexpectations, superdistributions and superquantiles with specialization to risk measures.