1. Approximation by quasi-interpolation operators and Smolyak's algorithm.
- Author
-
Kolomoitsev, Yurii
- Subjects
- *
SMOOTHNESS of functions , *BESOV spaces , *KERNEL functions , *PERIODIC functions , *ALGORITHMS - Abstract
We study approximation of multivariate periodic functions from Besov and Triebel–Lizorkin spaces of dominating mixed smoothness by the Smolyak algorithm constructed using a special class of quasi-interpolation operators of Kantorovich-type. These operators are defined similar to the classical sampling operators by replacing samples with the average values of a function on small intervals (or more generally with sampled values of a convolution of a given function with an appropriate kernel). In this paper, we estimate the rate of convergence of the corresponding Smolyak algorithm in the L q -norm for functions from the Besov spaces B p , θ s (T d) and the Triebel–Lizorkin spaces F p , θ s (T d) for all s > 0 and admissible 1 ≤ p , θ ≤ ∞ as well as provide analogues of the Littlewood–Paley-type characterizations of these spaces in terms of families of quasi-interpolation operators. [ABSTRACT FROM AUTHOR]
- Published
- 2022
- Full Text
- View/download PDF