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Multidimensional Iterative Interpolation

Published online by Cambridge University Press:  20 November 2018

Gilles Deslauriers ,
Jacques Dubois  and
Serge Dubuc
Gilles Deslauriers
Affiliation:
Département de mathématiques appliquées École Polytechnique, C.P. 6079, Succ. A Montréal, Québec, H3C 3A7
Jacques Dubois
Affiliation:
Département de mathématiques et d'informatique Université de Sherbrooke Sherbrooke, Québec, J1K2R1
Serge Dubuc
Affiliation:
Département de mathématiques et de statistique Université de Montréal, C.P. 6128, Succ. A, Montréal, Québec, H3C 3J7
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Abstract

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We define an iterative interpolation process for data spread over a closed discrete subgroup of the Euclidean space. We describe the main algebraic properties of this process. This interpolation process, under very weak assumptions, is always convergent in the sense of Schwartz distributions. We find also a convenient necessary and sufficient condition for continuity of each interpolation function of a given iterative interpolation process.

Keywords

Iterative interpolation processfundamental interpolating functioncharacteristic functioncontinuous interpolationtemperate distributionFourier transform65D0565D1026B0565Q0542A0542A38
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 43 , Issue 2 , 01 April 1991 , pp. 297 - 312
Copyright
Copyright © Canadian Mathematical Society 1991

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