We study approximation of multivariate periodic functions from Besov and Triebel–Lizorkin spaces dominating mixed smoothness by the Smolyak algorithm constructed using a special class quasi-interpolation operators Kantorovich-type. These are defined similar to classical sampling replacing samples with average values function on small intervals (or more generally sampled convolution given an app...

We study interpolation polynomials based on the points in [−1, 1]× [−1, 1] that are common zeros of quasi-orthogonal Chebyshev polynomials and nodes of near minimal degree cubature formula. With the help of the cubature formula we establish the mean convergence of the interpolation polynomials. 1991 Mathematics Subject Classification: Primary 41A05, 33C50.

Spline quasi-interpolants are local approximating operators for functions or discrete data. We consider the construction of discrete and integral spline quasi-interpolants on uniform partitions of the real line having small infinite norms. We call them near minimally normed quasi-interpolants: they are exact on polynomial spaces and minimize a simple upper bound of their infinite norms. We give...

We study approximation properties of general multivariate periodic quasi-interpolation operators, which are generated by distributions/functions φ˜j and trigonometric polynomials φj. The class such operators includes classical interpolation (φ˜j is the Dirac delta function), Kantorovich-type a characteristic scaling expansions associated with wavelet constructions, others. Under different compa...

We give a quasi-polynomial time algorithm for the problem of interpolating sparse polynomials over integer residue class ringsZm from their values given by a black box. This is a further development of [10].

We investigate the stability of Fredholm properties on interpolation scales of quasi-Banach spaces. This analysis is motivated by problems arising in PDE’s and several applications are presented.

The quasi-interpolation operators of Clément and Scott-Zhang type are generalized to the hp-context. New polynomial lifting and inverse estimates are presented as well.