A Jackson-type inequality associated with wavelet bases decomposition

Although wavelet decompositions of functions in Besov spaces have been extensively investigated, those involved with mild decay bases are relatively unexplored. In this paper, we study wavelet bases of Besov spaces and the relation between norms and wavelet coefficients. We establish the $l^{p}$ l p -stability as a measure of how effectively the Besov norm of a function is evaluated by its wavelet coefficients and the $L^{p}$ L p -completeness of wavelet bases. We also discuss wavelets with decay conditions and establish the Jackson inequality.

Quantum K-Theory of Grassmannians and Non-Abelian Localization

In the example of complex grassmannians, we demonstrate various techniques available for computing genus-0 K-theoretic GW-invariants of flag manifolds and more general quiver varieties. In particular, we address explicit reconstruction of all such invariants using finite-difference operators, the role of the q-hypergeometric series arising in the context of quasimap compactifications of spaces of rational curves in such varieties, the theory of twisted GW-invariants including level structures, as well as the Jackson-type integrals playing the role of equivariant K-theoretic mirrors.

On the best $L_2$-approximations of multivariable functions by means of splines

We obtain sharp inequalities of Jackson type for the best approximations of functions in $L_2(\mathbb{R}^m)$ by means of partial sums of wavelet series in case of multidimensional analogues of Shannon-Kotelnikov wavelets.

On sharp inequalities of Jackson type for entire functions in $L_2$

We conducted the research of sharp inequalities of Jackson type in $L_2$ space for approximation by entire functions of exponential type.

Behaviour of exact constants in inequalities of Jackson type

We studied the behaviour of exact constants in inequalities of Jackson type in $L_p$ space.

Inequalities of Jackson type for functions with values in Hilbert space

We present the generalization of M.I. Chernykh's results about the estimate of the best $L_2$-approximation of periodic function $f$ by trigonometric polynomials by its $L_2$-modulus of continuity, in the case of functions with values in Hilbert space.

On the best mean-square approximation by entire functions of finite type on the line

Jackson-type inequalities have been obtained for the best mean square approximation of differentiable functions by means of the entire functions of finite type on the line.

Advanced ordinary and fractional approximation by positive sublinear operators

Here we consider the ordinary and fractional approximation of functions by sublinear positive operators with applications to generalized convolution type operators expressed by sublinear integrals such as of Choquet and Shilkret ones. The fractional approximation is under fractional differentiability of Caputo, Canavati and Iterated-Caputo types. We produce Jackson type inequalities under basic initial conditions. So our way is quantitative by producing inequalities with their right hand sides involving the modulus of continuity of ordinary and fractional derivatives of the function under approximation. We give also an application related to Picard singular integral operators.