Approximation Theorems of Bernstein-Durrmeyer Operators in L_M~（Ba） Spaces

With the weighted modulus of smoothness as a metric,we prove the direct and the inverse theorems of approximation by Bernstein-Durrmeyer operators in LBa M spaces. Especially an approximation equivalent theorem of the operators is also obtained.     

The Boundedness of Calderón-Zygmund Operators by Wavelet Characterization

This article deals with the boundedness properties of Calderón-Zygmund operators on Hardy spaces Hp(Rn). We use wavelet characterization of Hp(Rn) to show that a Calderón-Zygmund operator T with T*1 = 0 is bounded on Hp(Rn), n/n+ε p ≤ 1, where ε is the regular exponent of kernel of T . This approach can be applied to the boundedness of operators on certain Hardy spaces without atomic decomposition or molecular characterization.     

Convergence of the q Analogue of Szász-Beta-Stancu Operators

In the present paper, we propose the q analogue of Sz a′sz-Beta-Stancu operators. By estimate the moments, we establish direct results in terms of the modulus of smoothness. Investigate the rate of point-wise convergence and weighted approximation properties of the q operators. Voronovskaja type theorem is also obtained.Our results generalize and supplement some convergence results of the q-Sz a′sz-Beta operators, thus they improve the existing results.     

Strong Converse Inequalities for Certain Mixed Szász-Beta Operators

In this paper,a strong converse inequality of type B in terms of a new Kfunctional Kλα f,t2（0 α 2,0 ≤ λ ≤ 1） for certain mixed Szász-Beta operators is given.By this inequality,the converse theorem can be obtained for the operators.     

Weighted Composition Followed and Proceeded by Differentiation Operators from Q_k(p,q)Space to Weighted α-Bloch Space

We study the boundedness and compactness of the weighted composition followed and proceeded by differentiation operators from Q_k(p,q)space to weighted α-Bloch space and little weighted α-Bloch space.Some necessary and sufficient conditions for the boundedness and compactness of these operators are given.     

Approximation by Complex Baskakov-Szsz-Durrmeyer Operators in Compact Disks

In this paper, we deal with the complex Baskakov-Szsz-Durrmeyer mixed operators and study Voronovskaja type results with quantitative estimates for these operators attached to analytic functions of exponential growth in DR= {z ∈ C;|z| R}.Also, the exact order of approximation is found. The method used allows to construct complex Szsz-type and Baskakov-type approximation operators without involving the values on [0, ∞).     

The approximate Jordan forms of operators on Σ_e~1 type Banach spaces

This paper studies the structure of operators on Σ1e type Banach spaces.It solves the problem of the small compact perturbations of operators with connected spectra.Namely,it shows that every operator with a connected spectrum on separable Σ1e type Banach spaces is a small compact perturbation of a strongly irreducible operator.Based on this result,this paper establishes the approximate Jordan forms of operators on Σ1e type Banach spaces with Schauder bases.     

Ambarzumyan Theorems for Dirac Operators

We consider the inverse eigenvalue problems for stationary Dirac systems with differentiable selfadjoint matrix potential.The theorem of Ambarzumyan for a Sturm-Liouville problem is extended to Dirac operators,which are subject to separation boundary conditions or periodic(semi-periodic)boundary conditions,and some analogs of Ambarzumyan's theorem are obtained.The proof is based on the existence and extremal properties of the smallest eigenvalue of corresponding vectorial Sturm-Liouville operators,which are the second power of Dirac operators.     

Some Approximation Properties of Certain q-Baskakov-Beta Operators

In this paper, we propose the q analogue of modified Baskakov-Beta opera-tors. The Voronovskaja type theorem and some direct results for the above operators are discussed. The rate of convergence and weighted approximation by the operators are studied.     

The spectrum of Bergman Toeplitz operators with some harmonic symbols

In this paper,we show that the spectrum of Toeplitz operators on the Bergman space with harmonic symbols of affine functions of z and  equals the image of closed unit disk under the symbol.Surprisingly this does not hold for Toeplitz operators with harmonic symbols of quadratic functions of z and .     

Approximation by Szasz-Mirakjan Type Operators in L''''

M.M.Derriennic discussed the properties of Bernstein-Durrmeyer operators,M. Heilmann solved the saturation situation and the author obtained the characte-rization of their order of approximation.As extending Kantorovich polynomials inL_p[0,1]to Szász-Mirakjan-Kantorovich operators in L_p[0,∞)by V.Totik,We in-troduce a new class of Szász-Mirakjan type operators:     

Approximation by the Modified q-Baskakov-Szsz Operators

In this paper we propose the q analogues of modified Baskakov-Sz′asz operators. We estimate the moments and established direct results in term of modulus of continuity. An estimate for the rate of convergence and weighted approximation properties of the q operators are also obtained.     

Some Remarks on the Restriction Theorems for the Maximal Operators on Rd

The aim of this paper is to give a simple proof of the restriction theorem for the maximal operators on the d-dimensional Euclidean space Rd, whose theorem was proved by Carro-Rodriguez in 2012.Moreover, we shall give some remarks of the restriction theorem for the linear and the multilinear operators by Carro-Rodriguez and Rodriguez, too.     

TOEPLITZ OPERATORS FROM HARDY SPACES TO WEIGHTED BERGMAN SPACES IN THE UNIT BALL OF Cn

We study Toeplitz operators from Hardy spaces to weighted Bergman spaces in the unit ball of Cⁿ.Toeplitz operators are closely related to many classical mappings,such as composition operators,the Volterra type integration operators and Carleson embeddings.We characterize the boundedness and compactness of Toeplitz operators from Hardy spaces H^p to weighted Bergman spaces A_α^q for the different values of p and q in the unit ball.     

Splitting of Operators and Operator Equations

In this paper,we consider the splitting operators into the product of two positive operators.For given operators A and T ∈ B(H) with A≥0 and ■,if T can be splitted as T=AX for some positive operator X,then the existence of X and the properties of T are studied.The related research are the solutions of operator equations T=XAX and TX=XAX,which have some particular properties and broad applications in many fields.The conditions for the existence of solutions or idempotent solutions of these kinds ...     

Simultaneous Approximation for Szsz-Mirakian-Stancu-Durrmeyer Operators

The aim of this work is to generalize Szsz-Mirakian operator in the sense of Stancu-Durrmeyer operators. We obtain approximation properties of these operators. Here we study asymptotic as well as rate of convergence results in simultaneous approximation for these modified operators.     

模糊粗糙群中的同态映射(英文)

This paper is devoted to the discussion of homomorphic properties of fuzzy rough groups.The fuzzy approximation space was generated by fuzzy normal subgroups and the fuzzy rough approximation operators were discussed in the frame of fuzzy rough set model.The basic properties of fuzzy rough approximation operators were obtained.     

On the ratio of different norms of caloric functions and related eigenfunctions of an integral operator

We investigate the ratio of L 1 and L 2 norms of the Cauchy problem solutions of heat equations with compact support initial data.The related asymptotic behavior of the eigenvalues and eigenfunctions of certain integral operators is obtained.     

The Estimates for Sharp Maximal Functions of Multilinear Strongly Singular Integral Operators

In this paper, the author obtains that the multilinear operators of strongly singular integral operators and their dual operators are bounded from some L^p（R^n） to L^p（R^n） when the m-th order derivatives of A belong to L^p（R^n） for r large enough. By this result, the author gets the estimates for the Sharp maximal functions of the multilinear operators with the m-th order derivatives of A being Lipschitz functions. It follows that the multilinear operators are （L^p, L^p）-type operators for 1 〈 p 〈 ∞.     

本刊英文版Vol.36(2020),No.11论文摘要(英文)

Diskcyclicity of Sets of Operators and Applications Mohamed AMOUCH Otmane BENCHIHEB Abstract In this paper,we introduce and study the diskcyclicity and disk transitivity of a set of operators.We establish a diskcyclicity criterion and give the relationship between this criterion and the diskcyclicity.As applications,we study the diskcyclicty of C0-semigroups and C-regularized groups.