One-point commuting difference operators of rank 1

One-point commuting difference operators of rank 1 are considered. The coefficients in such operators depend on one functional parameter, and the degrees of shift operators in difference operators are positive. These operators are studied in the case of hyperelliptic spectral curves, where the base point coincides with a point of branching. Examples of operators with polynomial and trigonometric coefficients are constructed. Operators with polynomial coefficients are embedded in differential operators with polynomial coefficients. This construction provides a new method for constructing commutative subalgebras in the first Weyl algebra.     

关于p-弱亚正规算子的一个注记

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Estimates on level set integral operators in dimension two

Both oscillatory integral operators and level set operators appear naturally in the study of properties of degenerate Fourier integral operators (such as generalized Randon transforms). The properties of oscillatory integral operators have a longer history and are better understood. On the other hand, level set operators, while sharing many common characteristics with oscillatory integral operators, are easier to handle. We study L²-estimates on level set operators in dimension two and compare them with what is known about oscillatory integral operators. The cases include operators with non-degenerate phase functions and the level set version of Melrose-Taylor transform (as an example of a degenerate phase function). The estimates are formulated in terms of the Newton polyhedra and type conditions.     

Semilinear evolution equations with nonlinear constraints and applications

This paper deals with a general class of evolution problems for semilinear equations coupled with nonlinear constraints. Those constraints may contain compositions of nonlinear operators and unbounded linear operators, and hence the associated operators are not necessarily formulated in the form of continuous perturbations of linear operators. Accordingly, a family of equivalent norms is introduced to discuss 'quasidissipativity' in a local sense of the operators and a generation theory for nonlinear semigroups is employed to construct solution operators on bounded sets. It is a feature of our treatment that the resultant solution operators are obtained as nonlinear semigroups on the whole space which are not 'quasicontractive' but locally equi-Lipschitz continuous.     

U-ideals of factorable operators

We suggest a method of renorming of spaces of operators which are suitably approximable by sequences of operators from a given class. Further we generalize J. Johnsons's construction of ideals of compact operators in the space of bounded operators and observe e.g. that under our renormings compact operators are u-ideals in the: space of 2-absolutely summing operators or in the space of operators factorable through a Hilbert space.     

Dirichlet空间上Toeplitz算子与Berezin型变换相关的一些性质

本文研究了单位圆盘D 的Dirichlet 空间上Toeplitz 算子和小Hankel 算子. 利用Berezin 型变换讨论了Toeplitz 算子的不变子空间问题, 具有Berezin 型符号的Toeplitz 算子的渐进可乘性以及Toeplitz 算子的Riccati 方程的可解性. 应用Berezin 变换得到了Toeplitz 算子和小Hankel 算子可逆的充分条件. 此外, 还利用Hankel 算子和Berezin 变换刻画了算子2T_uv-T_uT_v-T_vT_u 的紧性, 其中函数u,v ∈ L^2,1.     

A temporal database forecasting algebra

Though forecasting methods are used in numerous fields, we have seen no work on providing a general theoretical framework to build forecast operators into temporal databases, producing an algebra that extends the relational algebra. In this paper, we first develop a formal definition of a forecast operator as a function that satisfies a suite of forecast axioms. Based on this definition, we propose three families of forecast operators called deterministic, probabilistic, and possible worlds forecast operators. Additional properties of coherence, orthogonality, monotonicity, and fact preservation are identified that these operators may satisfy (but are not required to). We show how deterministic forecast operators can always be encoded as probabilistic forecast operators, and how both deterministic and probabilistic forecast operators can be expressed as possible worlds forecast operators. Issues related to the complexity of these operators are studied, showing the relative computational tradeoffs of these types of forecast operators. We explore the integration of different forecast operators with standard relational operators in temporal databases—including extensions of the relational algebra for the probabilistic and possible worlds cases—and propose several policies for answering forecast queries. Instances where these different forecast policies are equivalent have been identified, and can form the basis of query optimization in forecasting. These policies are evaluated empirically using a prototype implementation of a forecast query answering system and several forecast operators.     

Super-Ergodic operators

The aim of this work is to study operators naturally connected to Ergodic operators in infinite-dimensional Banach spaces, such as Uniform-Ergodic, Cesaro-bounded and Power-bounded operators, as well as stable and superstable operators. In particular, super-Ergodic operators are introduced and shown to be strictly between Ergodic and Uniform-Ergodic operators, and that any power bounded operator is super-Ergodic in a superreflexive space. New relationships between these operators are shown, others are proven to be optimal or can be ameliorated according to structural properties of the Banach space, such as the superreflexivity or with unconditional basis.

     

Banach 空间上算子的几种不可约性

本文根据Cowen-Douglas 算子的定义引入两类与强不可约算子有紧密联系的算子类— B_n 算子与B 算子. 说明了在可分Banach 空间上存在B_n 算子与B 算子. 文章详细讨论了几种具有不可约性的算子类之间的关系并得到了一个关系图. 本文还给出这些算子类的一些性质, 包括算子的(拟) 相似不变性等.     

Norm Inequalities for Fractional Integral Operators on Generalized Weighted Morrey Spaces

Considering a class of operators which include fractional integrals related to operators with Gaussian kernel bounds,the fractional integral operators with rough kernels and fractional maximal operators with rough kernels as special cases,we prove that if these operators are bounded on weighted Lebesgue spaces and satisfy some local pointwise control,then these operators and the commutators of these operators with a BMO functions are also bounded on generalized weighted Morrey spaces.     

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.     

Generalized random linear operators on a Hilbert space

In this paper, we are concerned with generalized random linear operators on a separable Hilbert space. Generalized random linear bounded operators, generalized random linear normal operators and generalized random linear self-adjoint operators are defined and investigated. The spectral theorems for generalized random linear normal operators and generalized random linear self-adjoint operators are obtained.     

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.     

A local lifting theorem for subnormal operators

Criteria for the existence of lifts of operators intertwining subnormal operators are established. The main result of the paper reduces lifting questions for general subnormal operators to questions about lifts of cyclic subnormal operators. It is shown that in general the existence of local lifts (i.e. those coming from cyclic parts) for a pair of subnormal operators does not imply the existence of a global lift. However this is the case when minimal normal extensions of subnormal operators in question are star-cyclic.

     

Norm Inequalities in Generalized Morrey Spaces

We prove that Calderón-Zygmund operators, Marcinkiewicz operators, maximal operators associated to Bochner-Riesz operators, operators with rough kernel as well as commutators associated to these operators which are known to be bounded on weighted Morrey spaces under appropriate conditions, are bounded on a wide family of function spaces.     

The construction and approximation of some neural networks operators

In this paper,the technique of approximate partition of unity is used to construct a class of neural networks operators with sigmoidal functions.Using the modulus of continuity of function as a metric,...     

半环中带算子的L-模糊h-理想

The notions of M-hemirings and L-fuzzy left h-ideals with operators in M-hemirings are introduced,and some properties are investigated.Given an L-fuzzy left h-ideal with operators,a new L-fuzzy left h-ideal with operators is established. Using a collection of left M-h-ideals,L-fuzzy left h-ideais with operators are con- structed.Moreover,the concept of M-Notherian M-hemiring is introduced and its characterization is given.     

The Theory of Operators with Dominant Main Diagonal. I.

In this paper a characterization of the symmetric operators on a finite dimensional Hilbert space which have a matrix representation with a dominant diagonal with respect to any orthonormal basis are obtained. The set of such operators is a solid, reproducing, normal and acute cone in the space of symmetric operators. These results are applied to localizing the spectrum of operators pencils.     

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.     

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.