Approximation by multiinteger translates of functions having global support
Journal of Approximation Theory
On local and controlled approximation order
Journal of Approximation Theory
A new version of the Strang-Fix conditions
Journal of Approximation Theory
On approximation by translates of globally supported functions
Journal of Approximation Theory
Simultaneous approximation from PSI spaces
Journal of Approximation Theory
Coordinate order of approximation by functional-based approximation operators
Journal of Approximation Theory
Approximation from shift-invariant spaces by integral operators
SIAM Journal on Mathematical Analysis
On the approximation order of principal shift-invariant subspaces of LpRd
Journal of Approximation Theory
Construction techniques for highly accurate quasi-interpolation operators
Journal of Approximation Theory
Radial Basis Functions
Approximation orders of shift-invariant subspaces of W2s(Rd)
Journal of Approximation Theory
Approximation with scaled shift-invariant spaces by means of quasi-projection operators
Journal of Approximation Theory
Constructive realization of dual systems for generators of multi-window spline-type spaces
Journal of Computational and Applied Mathematics
Hi-index | 0.02 |
We derive new convergence results for the Schoenberg operator and more general quasi-interpolation operators. In particular, we prove that natural conditions on the generator function imply convergence of these operators in the Fourier algebra A(R^d)=FL^1(R^d) and in S"0(R^d), a function space developed by the first author and often used in time-frequency analysis. As a simple yet very useful consequence for applications in Gabor analysis we obtain that piecewise linear interpolation converges in A(R) as well as in S"0(R). Generally, the results presented in this paper are motivated by discretization problems arising in time-frequency analysis and have important consequences in this field.