Jaroslav Kurzweil

Topological equivalence and structural stability for linear difference equations

Abstract In this paper first we prove that if two linear difference equations with invertible coefficient matrices are topologically equivalent and one of them has bounded coefficient matrix together with its inverse, then the coefficient matrix of the other equation is also bounded together with its inverse. We also prove that if a linear difference equation with bounded and invertible coefficient matrix is structurally stable then the inverse of the coefficient matrix is also bounded.

Henstock-Kurzweil integration : its relation to topological vector spaces

Integrable functions and their primitives gauges and Borel measurability convergence an abstract setting an abstract setting with D countable locally convex topologies tolerant to Q-convergence topological vector spaces tolerant to Q-convergence P as a complete topological vector space open problems.

Another Perron type integration in n dimensions as an extension of integration of stepfunctions

AbstractFor a new Perron-type integral a concept of convergence is introduced such that the limit f of a sequence of integrable functions

Generalized ordinary differential equations and continuous dependence on a parameter

f_k ,k \in \mathbb{N}

Ordinary differential equations

is integrable and any integrable f is the limit of a sequence of stepfunctions

Differentiability and Integrability in n Dimensions with Respect to α-Regular Intervals

g_k ,k \in \mathbb{N}