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Approximation and spectral properties of periodic spline operators

Published online by Cambridge University Press:  20 January 2009

S. L. Lee  and
W. S. Tang
S. L. Lee
Affiliation:
Department of MathematicsNational University of Singapore10 Kent Ridge CrescentSingapore 0511
W. S. Tang
Affiliation:
Department of MathematicsNational University of Singapore10 Kent Ridge CrescentSingapore 0511
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Abstract

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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

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