𝔖 Bobbio Scriptorium
✦   LIBER   ✦

Asymptotic Formulas for Convolution Operators with Spline Kernels

✍ Scribed by S.L. Lee; R. Osman

Publisher
Elsevier Science
Year
1995
Tongue
English
Weight
532 KB
Volume
83
Category
Article
ISSN
0021-9045

No coin nor oath required. For personal study only.

✦ Synopsis

We derive asymptotic formulas for convolution operators with spline kernels for differentiable functions. These formulas are analogous to Bernstein's extension of Voronovskaya's results on Bernstein polynomials for functions with higher order derivatives. Two classes of operators are considered, viz., the de la VallΓ©e PoussinSchoenberg operators with trigonometric spline kernels and the singular integrals of Riemann-Lebesgue with periodic polynomial spline kernels. The former includes the de la VallΓ©e means as a special case. 1995 Academic Press. Inc

πŸ“œ SIMILAR VOLUMES

Spline Approximation Methods with Unifor
Spline Approximation Methods with Uniform Meshes in Algebras of Multiplication and Convolution Operators
✍ Pedro A. Santos πŸ“‚ Article πŸ“… 2001 πŸ› John Wiley and Sons 🌐 English βš– 375 KB πŸ‘ 1 views

The purpose of this paper is to obtain necessary and sufficient conditions for maximum defect spline approximation methods with uniform meshes to be stable. The methods are applied to operators belonging to the closed subalgebra of L(L 2 (IR)) generated by operators of multiplication by piecewise co

Some Estimates for Radial Fourier Multip
Some Estimates for Radial Fourier Multiplier Operators with Slowly Decaying Kernels
✍ Jay Epperson πŸ“‚ Article πŸ“… 1998 πŸ› John Wiley and Sons 🌐 English βš– 503 KB

We consider the restriction to radial functions of a class of radial Fourier multiplier operators containing the Bochner-Ftiesz multiplier operator. The convolution kernel K ( z ) of an operator in this class decays too slowly at infinity to be integrable, but has enough oscillation to achieve LP-bo