Изучается процедура построения функции Лагранжа для интерполяции на
равномерной сетке с гауссовыми функциями. Показано, что с ростом дисперсии …

В работе изучаются однопараметрические семейства целочисленных сдвигов функций
Гаусса и Лоренца. В случае функции Лоренца получены формулы для коэффициентов …

This article addresses two topics of significant mathematical and practical interest in the
theory of kernel approximation: the existence of local and stable bases and the L_p …

In this paper, one-parameter families of integer translates of the Gaussian and Lorentz
functions are studied. For a Lorentz function, we obtain formulas for the coefficients of the …

In this paper, we study the sampling and average sampling problem in a quasi shift-invariant
space VX (φ), where X is a discrete subset of R and φ is a continuously differentiable …

A Riesz-basis sequence for L 2 [− π, π] is a strictly increasing sequence X:=(xj) j∈ Z in R
such that the set of functions (e− ixj (⋅)) j∈ Z is a Riesz basis for L 2 [− π, π]. Given such a …

The structure of certain types of quasi shift-invariant spaces, which take the form V (ψ, X):=
span‾ L 2 {ψ (⋅− xj): j∈ Z} for an infinite discrete set X=(xj)⊂ R is investigated. Additionally …

We provide sufficient conditions on a family of functions (ϕ α) α∈ A: R d→ R for sampling of
multivariate bandlimited functions at certain nonuniform sequences of points in R d. We …

In this paper, we prove that any f belongs to a shift-invariant space V (ϕ) can be
reconstructed uniquely and stably from its local averages on some discrete sets, where the …

This article pertains to interpolation of Sobolev functions at shrinking lattices h ℤ d hZ^d from
L p shift-invariant spaces associated with cardinal functions related to general multiquadrics …