希尔伯特空间有限区域成像积分算子的谱

本文讨论了希尔伯特空间中有限区域成像积分算子的本征值和本征函数,研究了非对称核的情形,并用微扰和有限秩方法计算了衍射受限和离焦情况下的本征值和本征函数。     

Symmetries of nonlinear hyperbolic systems of the Toda chain type

We consider hyperbolic systems of equations that have full sets of integrals along both characteristics. The best known example of models of this type is given by two-dimensional open Toda chains. For systems that have integrals, we construct a differential operator that takes integrals into symmetries. For systems of the chosen type, this proves the existence of higher symmetries dependent on arbitrary functions. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 155, No. 2, pp. 344–355, May, 2008.     

A new reverse Hilbert-type inequality with a best constant factor

In this paper, we give a new reverse Hilbert-type inequality with a best constant factor and some parameters. As application, we consider the equivalent form and some particular results.     

A regularization of nonlinear diffusion equations in a multiresolution framework

We develop a regularization technique for Perona–Malik diffusion equations that relies on multiresolution techniques. The main result of this paper is to show that the chosen discretization overcomes the ill posedness of the nonlinear Perona–Malik model. The resulting algorithm is tested and the results are compared with pixel‐based methods. Copyright © 2007 John Wiley & Sons, Ltd.     

Hard-sphere binary-collision operators

The time displacement operator is described for a system of hard-sphere particles. We show how to avoid needing a representation for this operator in unphysical regions of phase space, and how to construct a useful representation in terms of binary collision operators in the physical region. The various binary collision operators used for hard-sphere systems are derived for the case of a system of two spheres, and the results are generalized toN-particle systems.Dedicated to Prof. E. G. D. Cohen on the occasion of his 65th birthday.     

Boundary integral equations in time-dependent bending of thermoelastic plates

The initial-boundary value problems with the Dirichlet and Neumann boundary conditions arising in the theory of bending of thermoelastic plates with transverse shear deformation are reduced to time-dependent boundary integral equations by means of layer potentials. The solvability of these equations is then investigated in Sobolev-type spaces.     

Variational principles for symmetric bilinear forms

Every compact symmetric bilinear form B on a complex Hilbert space produces, via an antilinear representing operator, a real spectrum consisting of a sequence decreasing to zero. We show that the most natural analog of Courant's minimax principle for B detects only the evenly indexed eigenvalues in this spectrum. We explain this phenomenon, analyze the extremal objects, and apply this general framework to the Friedrichs operator of a planar domain and to Toeplitz operators and their compressions. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Approximation of finite-section equations by piecewise constant functions

The problem is studied of reducing the amount of discrete information required for achieving a prescribed accuracy of solving Fredholm integral equations of the first kind on a half-line. The equations are solved by the finite-section method combined with piecewise constant interpolation of the kernel and the right-hand side at uniform grid points. The approximating properties of the discretization schemes are examined, and the corresponding computational costs are analyzed.     

Function-valued Padé-type approximant via the formal orthogonal polynomials and its applications in solving integral equations

A kind of function-valued Padé-type approximant via the formal orthogonal polynomials (FPTAVOP) is introduced on the polynomial space and an algorithm is sketched by means of the formal orthogonal polynomials. This method can be applied to approximate characteristic values and the corresponding characteristic function of Fredholm integral equation of the second kind. Moreover, theoretical analyses show that FPTAVOP method is the most effective one for accelerating the convergence of a sequence of functions. In addition, a typical numerical example is presented to illustrate when the estimates of characteristic value and characteristic function by using this new method are more accurate than other methods.     

Defining Relations for W-Algebras from Singular Vectors

It is shown that the commutation relations of W-algebras can be recovered from the singular vectors of their simplest nontrivial, completely degenerate highest weight representation.