Cardinal translation invariant Tchebycheffian B-splines

N. Dyn; A. Ron

doi:10.1007/BF02836156

Cardinal translation invariant Tchebycheffian B-splines

N. Dyn^*, A. Ron

^*Corresponding author for this work

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

Cardinal Tchebycheffian B-splines, defined by weight functions of the form {Mathematical expression} with {Mathematical expression}, are investigated. It is shown that these B-splines are translation invariant, have a geometric representation and satisfy a generalized Hermite-Genocchi formula. For pure exponential weight functions the above results lead to a product type expression for the Fourier transform of the cardinal exponential B-splines, showing that these functions are convolutions of lower order ones. Similar conclusions are obtained for the corresponding Greens' functions.

Original language	English
Pages (from-to)	1-12
Number of pages	12
Journal	Approximation Theory and Its Applications
Volume	6
Issue number	2
DOIs	https://doi.org/10.1007/BF02836156
State	Published - Jun 1990

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abstract = "Cardinal Tchebycheffian B-splines, defined by weight functions of the form {Mathematical expression} with {Mathematical expression}, are investigated. It is shown that these B-splines are translation invariant, have a geometric representation and satisfy a generalized Hermite-Genocchi formula. For pure exponential weight functions the above results lead to a product type expression for the Fourier transform of the cardinal exponential B-splines, showing that these functions are convolutions of lower order ones. Similar conclusions are obtained for the corresponding Greens' functions.",

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AB - Cardinal Tchebycheffian B-splines, defined by weight functions of the form {Mathematical expression} with {Mathematical expression}, are investigated. It is shown that these B-splines are translation invariant, have a geometric representation and satisfy a generalized Hermite-Genocchi formula. For pure exponential weight functions the above results lead to a product type expression for the Fourier transform of the cardinal exponential B-splines, showing that these functions are convolutions of lower order ones. Similar conclusions are obtained for the corresponding Greens' functions.

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Cardinal translation invariant Tchebycheffian B-splines

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