Existence of Solutions for a Class of Quasi-Linear Singular Integro-Differential Equations

2000 Mathematics Subject Classification: 45F15, 45G10, 46B38.

Spectra of Ruelle Transfer Operators for Contact Flows

In this survey article we discuss some recent results concerning strong spectral estimates for Ruelle transfer operators for contact flows on basic sets similar to these of Dolgopyat obtained in the case of Anosov flows with C1 stable and unstable foliations. Some applications of Dolgopyat's results and the more recent ones are also described.

Weighted Approximation by a Class of Bernstein-Type Operators

AMS classification: 41A36, 41A10, 41A25, 41Al7.

Triangular Models and Asymptotics of Continuous Curves with Bounded and Unbounded Semigroup Generators

2000 Mathematics Subject Classification: Primary 47A48, Secondary 60G12.

Compactness in the First Baire Class and Baire-1 Operators

For a polish space M and a Banach space E let B1 (M, E) be the space of first Baire class functions from M to E, endowed with the pointwise weak topology. We study the compact subsets of B1 (M, E) and show that the fundamental results proved by Rosenthal, Bourgain, Fremlin, Talagrand and Godefroy, in case E = R, also hold true in the general case. For instance: a subset of B1 (M, E) is compact iff it is sequentially (resp. countably) compact, the convex hull of a compact bounded subset of B1 (M, E) is relatively compact, etc. We also show that our class includes Gulko compact. In the second part of the paper we examine under which conditions a bounded linear operator T : X ∗ → Y so that T |BX ∗ : (BX ∗ , w∗ ) → Y is a Baire-1 function, is a pointwise limit of a sequence (Tn ) of operators with T |BX ∗ : (BX ∗ , w∗ ) → (Y, · ) continuous for all n ∈ N. Our results in this case are connected with classical results of Choquet, Odell and Rosenthal.

On Two Saigo’s Fractional Integral Operators in the Class of Univalent Functions

2000 Mathematics Subject Classification: Primary 26A33, 30C45; Secondary 33A35

Bounds for Fractional Powers of Operators in a Hilbert Space and Constants in Moment Inequalities

Mathematics Subject Classification: 47A56, 47A57,47A63

Linear Colligations and Dynamic System Corresponding to Operators in the Banach Space

2000 Mathematics Subject Classification: Primary 47A48, 93B28, 47A65; Secondary 34C94.

Examples Illustrating some Aspects of the Weak Deligne-Simpson Problem

Research partially supported by INTAS grant 97-1644

Integral Manifolds and Bounded Solutions of Singularly Perturbed Systems of Impulsive Differential Equations

Sufficient conditions for the existence of bounded solutions of singularly perturbed impulsive differential equations are obtained. For this purpose integral manifolds are used.

Automata–based Method for Solving Systems of Linear Constraints in {0,1}

We consider a finite state automata based method of solving a system of linear Diophantine equations with coefficients from the set {-1,0,1} and solutions in {0,1}.

Generalized Sobolev Spaces of Exponential Type Associated with the Dunkl Operators

2000 Mathematics Subject Classification: 35E45

On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

Properties of Lp (K)-Solutions of Linear Nonhomogeneous Impulsive Differential Equations with Unbounded Linear Operator

Sufficient conditions for the existence of Lp(k)-solutions of linear nonhomogeneous impulsive differential equations with unbounded linear operator are found. An example of the theory of the linear nonhomogeneous partial impulsive differential equations of parabolic type is given.

On some Modifications of the Nekrassov Method for Numerical Solution of Linear Systems of Equations

A modification of the Nekrassov method for finding a solution of a linear system of algebraic equations is given and a numerical example is shown.