Article contents
Approximation and spectral properties of periodic spline operators
Published online by Cambridge University Press: 20 January 2009
Abstract
We consider discrete convolution operators whose range is the k-dimensional space spanned by the translates of a single function. Examples of include the space of trigonometric polynomials, periodic polynomial splines and trigonometric splines. The eigenfunctions of these operators corresponding to the nonzero eigenvalues are independent of α, and they form an orthogonal basis for . The limiting behaviour of as α, k→∞, is also considered. The corresponding limiting semigroups are computed explicitly.
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 3 , October 1991 , pp. 363 - 382
- Copyright
- Copyright © Edinburgh Mathematical Society 1991
References
REFERENCES
- 3
- Cited by