On h-unitary and block-toeplitz h-normal operators

A special class of normal operators acting in spaces with indefinite scalar products is studied. The operators from this class are characterized by the property that, in a natural basis, their matrices have diagonal block-Toeplitz forms. The relations between polynomials of self-adjoint operators and operators from this class are established.     

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.     

On a class of completely continuous operators in Hilbert spaces

We introduce a class G of completely continuous operators and prove theorems on the spectral structure of these operators. In particular, operators of this class are similar to model operators in de Branges spaces.     

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…     

Asymptotic Toeplitz and Hankel operators on the Bergman space

In this paper the concept of asymptotic Toeplitz and asymptotic Hankel operators on the Bergman space are introduced and properties of these classes of operators are studied. The importance of this notion is that it associates with a class of operators a Toeplitz operator and with a class of operators a Hankel operator where the original operators are not even Toeplitz or Hankel. Thus it is possible to assign a symbol to an operator that is not Toeplitz or Hankel and hence a symbol calculus is obtained. Further a relation between Toeplitz operators and little Hankel operators on the Bergman space is established in some asymptotic sense.     

关于p-弱亚正规算子的一个注记

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多线性分数次积分算子的一致有界性

研究了Lebesgue空间上多线性分数次积分算子和相应的多线性分数次极大算子的有界性,利用多线性分数次积分转化为相对应的分数次积分的方法来讨论,得到算子TΩ,α,A1,A2和MΩ,α,A1,A2的(Lp,Lq)的一致L ipsch itz估计,获得一种简明的方法.     

On singular integrals related to the Littlewood-Paley inequality for arbitrary intervals

The proof of the inequality mentioned in the title requires the knowledge of the fact that operators of a certain class are Calderón-Zygmund singular integral operators. We slightly extend this class. Bibliography: 4 titles. __________ Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 345, 2007, pp. 113–119.     

Convolution equations of the first kind on a finite interval in Sobolev spaces

The study of a class of operators associated with convolution equations of the first kind on a finite interval is reduced to the study of Wiener-Hopf operators with piecewise continuous symbol on R. Fredholm properties and invertibility conditions for this class of operators are investigated. An example from diffraction theory is considered.Sponsored by J.N.I.C.T. (Portugal) under grant n ^o 87422/MATM.     

The new approximation operators with sigmoidal functions

The aim of this paper is to investigate approximation operators with logarithmic sigmoidal function of a class of two neural networks weights and a class of quasi-interpolation operators. Using these operators as approximation tools, the upper bounds of estimate errors are estimated for approximating continuous functions.     

Hardy空间上一类$m$-复对称Toeplitz算子

本文主要研究Toeplitz算子相对于一对置换的共轭算子是2-复对称的充要条件. 首先在经典的Hardy空间上介绍一类被称为一对置换的共轭算子, 其次完整地刻画了在这类共轭算子下Toeplitz算子是2-复对称的结构, 利用Toeplitz算子在Hardy空间的经典正规正交基下的矩阵表示来刻画2-复对称Toeplitz算子. 最后对于Toeplitz算子分别补充前提$f_n=-f_{-n}$和$f_n=f_{-n}$, 得到了更简化的结果. 在第二个前提下, 研究Toeplitz算子的3-复对称性, 得到$T_f$关于$C_{(i,j)}$是3-CSO的结果和是2-CSO相同.     

Shape Derivatives of Boundary Integral Operators in Electromagnetic Scattering. Part I: Shape Differentiability of Pseudo-homogeneous Boundary Integral Operators

In this paper we study the shape differentiability properties of a class of boundary integral operators and of potentials with weakly singular pseudo-homogeneous kernels acting between classical Sobolev spaces, with respect to smooth deformations of the boundary. We prove that the boundary integral operators are infinitely differentiable without loss of regularity. The potential operators are infinitely shape differentiable away from the boundary, whereas their derivatives lose regularity near the boundary. We study the shape differentiability of surface differential operators. The shape differentiability properties of the usual strongly singular or hypersingular boundary integral operators of interest in acoustic, elastodynamic or electromagnetic potential theory can then be established by expressing them in terms of integral operators with weakly singular kernels and of surface differential operators.     

On nonlinear nuclear operators

A class of operators is introduced and referred to as nonlinear nuclear operators. As in the case of linear nuclear operators this class of nonlinear operators is defined by means of a tensor product of two topological vector spaces. It is then shown that, as in the linear case, a series representation of the operator is valid. The deviation of the nonlinear theory from the linear case is discussed and an example in the framework of generalized stochastic processes is given.     

Weyl-type theorems for unbounded posinormal operators

For bounded linear operators, the study ofWeyl-type theorems and properties has been of significant interest for several non-normal classes of operators. In this paper, we extend this study to a class of unbounded posinormal operators. We define and study the spectral properties of unbounded posinormal and totally posinormal operators defined on an infinite dimensional complex Hilbert space H. For this class, under certain conditions several Weyl-type theorems and related properties are obtained.     

On the calculation of the spectra of directionally perturbed operators

A class of operators with special spectral properties is defined. An operator in this class is fairly simple, acts in a separable Hilbert space, and can be perturbed so that an a priori given function from its domain is an eigenfunction of the perturbed operator. This fact is shown to be useful for constructing operators in mathematical physics. Specific examples are given.     

Non-Archimedean Pseudodifferential Operators and Feller Semigroups

In this article we study a large class of non-Archimedean pseudodifferential operators whose symbols are negative definite functions.We prove that these operators extend to generators of Feller semigroups. In order to study these operators, we introduce a new class of anisotropic Sobolev spaces, which are the natural domains for the operators considered here.We also study the Cauchy problem for certain pseudodifferential equations.     

On some properties of a class of degenerate pseudodifferential operators

A new class of pseudodifferential operators with degeneration is considered. The operators are constructed using a special integral transform mapping a weighted differentiation operator to a multiplication operator. The composition and boundedness properties of such operators in special weighted spaces are examined. Theorems on commutation of such operators with differentiation operators are obtained. The behavior of these operators as t → 0and t → +∞ is investigated. The properties of adjoint operators are studied, and an analogue of Gårding’s inequality is proved.     

Localization results for generalized Baskakov/Mastroianni and composite operators

In this paper we study localization results for classical sequences of linear positive operators that are particular cases of the generalized Baskakov/Mastroianni operators and also for certain class of composite operators that can be derived from them by means of a suitable transformation. Amongst these composite operators we can find classical sequences like the Meyer-König and Zeller operators and the Bleimann, Butzer and Hahn ones. We extend in different senses the traditional form of the localization results that we find in the classical literature and we show several examples of sequences with different behavior to this respect.     

On a Class of Non-local Operators in Conformal Geometry

In this expository article, the authors discuss the connection between the study of non-local operators on Euclidean space to the study of fractional GJMS operators in conformal geometry. The emphasis is on the study of a class of fourth order operators and their third order boundary operators. These third order operators are generalizations of the Dirichlet-to-Neumann operator.