Scientific research sphere is approximation theory. The main investigation directions are geometrical approximation theory, mapping smoothing in infinite and finite dimensional Banach spaces, smooth selections from multi-valued mappings, different topological questions in infinite dimensional Banach spaces and a number of classical questions in approximation theory.

In geometric approximation theory interest lies in the field of Chebyshev sets and their generalizations. In the last time this direction is under intensive research in connection with the necessity of approximation theory numerous non-linear objects structural and approximate properties investigation. Among the objects there are differential equations decisions sets, bilinear forms sets, splines with non-fixed knots and etc. The most important for the non-linear objects questions are the best approximation elements existence, uniqueness and stability (regularity) problems.

Infinite spaces Banach approximation theory is relatively new branch of approximation theory. Smoother mapping approximation possibility investigation is often reduced to Banach space geometry and functional analysis fine questions and is useful in interesting topological applications in these spaces as means for research. Infinite space smoothing problem decisions are applicable for smoothing in spaces of finite, but rather big dimension n, where depending on n behavior of smoothing functions is very essential. This theory is found to be connected with Banach spaces convex-valued mappings smooth selections problems.

In classical approximation theory field functional classes width problems, Jackson-Stechkin and Whitney type inequalities, linear and non-linear extensions multivariate functions questions are of the most interest. In these multiparameters problems the corresponding values (of width, of Jackson and Whitney constants) behavior, depending on approximate objects dimensional and smoothing characteristic, is investigated.

Welcome to special functional theory and approximation seminar!