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.     

On the explicit formulas for zeta functions

In this paper, we study the properties of a large class of zeta functions that arises in geometric analysis and mathematical physics. They are attached to some elliptic operators. This method can be used to evaluate explicitly the special values of zeta functions of elliptic operators defined on some symmetric 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.     

Approximation of Mappings with Values Which Are Upper Semicontinuous Functions

In this paper we study some aspects of the approximation of mappings taking values in a special class of upper semicontinuous functions. Some Korovkin type theorems for positive linear operators are obtained, and consequences of these theorems for a special class of operators defined through partial sum stochastic processes are analyzed.     

Trace formula for a perturbed operator of Jacobi type

There is a broad class of problems of mathematical physics that lead to the solution of second-order differential equations of some special form. In particular, systems of solutions of such equations are given by classical polynomials (Jacobi, Laguerre, and Hermite polynomials). Such equations are naturally related to second-order differential operators in appropriate Hilbert spaces and the corresponding spectral problems. We consider a Jacobi operator and its perturbation by the operator of multiplication by a function. We derive a trace formula for the perturbed operator and a closed-form expression for the first correction.     

一类非线性算子的满射性

Hilbert空间中余弦值不为1的非线性算子构成了一类广泛的特殊的非线性算子.研究了这类非线性算子的满射性,并给出了其成立的几个充分条件.     

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.     

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 One Class of Matrix Differential Operators

We consider one class of matrix differential operators in the whole space. For this class of operators we establish the isomorphic properties in some special scales of weighted Sobolev spaces and study the regularity properties for solutions to the system of differential equations defined by these operators. The class of operators under consideration contains the stationary Navier–Stokes operator.     

Isomorphic Properties of One Class of Differential Operators and Their Applications

We consider a special class of quasielliptic matrix operators and establish isomorphic properties of these operators in special scales of weighted Sobolev spaces. We give an example of application of these results to systems of differential equations that are not solved with respect to the derivative.     

A characterization of boundary conditions yielding maximal monotone operators

We provide a characterization for maximal monotone realizations for a certain class of (nonlinear) operators in terms of their corresponding boundary data spaces. The operators under consideration naturally arise in the study of evolutionary problems in mathematical physics. We apply our abstract characterization result to Port–Hamiltonian systems and a class of frictional boundary conditions in the theory of contact problems in visco-elasticity.     

On a Multivariable Class of Mittag-Leffler Type Functions

The present paper studies and investigates a class of Mittag-Leffler type multivariable functions. We derive the necessary convergence conditions and establish several properties associated with this class and those related with the corresponding class of fractional integral operators. New extensions of the introduced definitions and special cases of some of the results are also pointed out.     

POWERS OF AN INVERTIBLE （s,p） - ω-HYPONORMAL OPERATOR

It is known that the square of a ω-hyponormal operator is also ω-hyponormal. For any 0〈 p 〈 1, there exists a special invertible operator such that all of its integer powers are all p - ω-hyponormal. In this article, the author introduces the class of （s, p） -ω-hyponormal operators on the basis of the class of p- ω-hyponormal operators. For s 〉0, 0 〈 p 〈 1, the author gives a characterization of （s,p） -ω-hyponormal operatots; the author shows that all integer powers of special （s, p） -ω-hyponormal operators are （s,p） -ω-hyzponormal.     

Generalized OWA Aggregation Operators

We extend the ordered weighted averaging (OWA) operator to a provide a new class of operators called the generalized OWA (GOWA) operators. These operators add to the OWA operator an additional parameter controlling the power to which the argument values are raised. We look at some special cases of these operators. One important case corresponds to the generalized mean and another special case is the ordered weighted geometric operator.     

Minimization of a functional over the set of causal operators of causal Hilbert space

The minimization problem for a quadratic functional defined on the set of nonwarning (causal) operators acting in a causal Hilbert space can be regarded as an abstrat analog of the Wiener problem on constructing the optimal nonwarning filter. A similar problem also arises in the linear control problem with the quadratic performance criterion (in this case the transfer operators of a closed control system serve as causal ones). The introduction of causal operators in filtering theory and control theory is a mathematical expression of the causality principle, which must be taken into account for a number of problems. In the present paper we attempt to systematize the mathematical foundations of the abstract linear filtering theory, for which its basic results are expressed in terms of operators describing the filtering problem. We introduce and study a class of finite operators, a natural generalization of the class of causal operators, and give a solution of the minimization problem for a quadratic positive functional defined on the set of causal operators acting in a “discrete” causal space. Bibliography: 54 titles. Translated fromProblemy Matematicheskogo Analiza, No. 14, 1995. pp. 143–187.     

Monotonicity conditions for a class of quasilinear differential operators depending on parameters

A special class of quasilinear differential operators depending on a finite number of parameters is introduced and necessary and sufficient monotonicity conditions for such operators are found.     

On a class of operators on Hilbert space with applications to factorization and systems theory

A class of operators is defined in a Hilbert resolution space setting that offers a new perspective on problems of causal invertibility, special factorization, and the theory of quadratic cost optimization problems for dynamical systems. The major results include an extension of the special factorization to a class of noncompact operators and the definition of an abstract state space. These results are then used to obtain an optimal feedback solution to an abstract linear regular-quadratic cost problem.     

Multidimensional modified fractional calculus operators involving a general class of polynomials

In the present work, we introduce and study essentially a class of multi-dimensional modified fractional calculus operators involving a general class of polynomials in the kernel. These operators are considered in the space of functionsM _γ (R ₊ ⁿ ). Some mapping properties and fractional differential formulas are obtained. Also images of some elementary and special functions are established.