Displaying similar documents to “Linear integral equations in the space of regulated functions”

Spectral properties of fourth order differential operators

Ondřej Došlý, Roman Hilscher (1997)

Mathematica Bohemica

Similarity:

Necessary and sufficient conditions for discreteness and boundedness below of the spectrum of the singular differential operator ℓ ( y ) ≡ 1 w ( t ) ( r ( t ) y ) , t ∈ [ a , ∞ ) are established. These conditions are based on a recently proved relationship between spectral properties of ℓ and oscillation of a certain associated second order differential equation.

On systems of linear algebraic equations in the Colombeau algebra

Jan Ligęza, Milan Tvrdý (1999)

Mathematica Bohemica

Similarity:

From the fact that the unique solution of a homogeneous linear algebraic system is the trivial one we can obtain the existence of a solution of the nonhomogeneous system. Coefficients of the systems considered are elements of the Colombeau algebra ℝ ¯ of generalized real numbers. It is worth mentioning that the algebra ℝ ¯ is not a field.

On special Riemannian 3 -manifolds with distinct constant Ricci eigenvalues

Oldřich Kowalski, Zdeněk Vlášek (1999)

Mathematica Bohemica

Similarity:

The first author and F. Prufer gave an explicit classification of all Riemannian 3-manifolds with distinct constant Ricci eigenvalues and satisfying additional geometrical conditions. The aim of the present paper is to get the same classification under weaker geometrical conditions.

Linear Stieltjes integral equations in Banach spaces

Štefan Schwabik (1999)

Mathematica Bohemica

Similarity:

Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in []. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. []). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the...

The behaviour of the nonwandering set of a piecewise monotonic interval map under small perturbations

Peter Raith (1997)

Mathematica Bohemica

Similarity:

In this paper piecewise monotonic maps T [ 0 , 1 ] → [ 0 , 1 ] are considered. Let Q be a finite union of open intervals, and consider the set R ( Q ) of all points whose orbits omit Q . The influence of small perturbations of the endpoints of the intervals in Q on the dynamical system ( R ( Q ) , T ) is investigated. The decomposition of the nonwandering set into maximal topologically transitive subsets behaves very unstably. Nonetheless, it is shown that a maximal topologically transitive subset cannot be completely destroyed...