On positivity properties of fundamental cardinal polysplines
Optimal quadrature formulas in the sense of Nikolski.
Pointwise inequalities for Sobolev functions and some applications
We get a class of pointwise inequalities for Sobolev functions. As a corollary we obtain a short proof of Michael-Ziemer’s theorem which states that Sobolev functions can be approximated by functions both in norm and capacity.
Quadrature over the sphere.
Representation formulae for (C₀) m-parameter operator semigroups
Some general representation formulae for (C₀) m-parameter operator semigroups with rates of convergence are obtained by the probabilistic approach and multiplier enlargement method. These cover all known representation formulae for (C₀) one- and m-parameter operator semigroups as special cases. When we consider special semigroups we recover well-known convergence theorems for multivariate approximation operators.
Shift invariant operators and a saturation theorem
The properties of shift invariant operators are proved: It is shown that Q has polynomial order r iff r is the rate of convergence of . A weak saturation theorem is given. If f is replaced by in the weak saturation formula the asymptotics of the expression is calculated. Moreover, bootstrap approximation is introduced.
Some inequalities connected with an approximate integration.
Two Korovkin-type theorems in multivariate approximation.
Приближение экспоненты и относительная близость устойчивых сигналов