Exponential B-splines and the partition of unity property

Authors:
Ole Christensen;Peter Massopust
Affiliations:
Department of Mathematics, Technical University of Denmark, Lyngby, Denmark 2800;Institute for Biomathematics and Biometry, Helmholtz Zentrum München, München, Germany and Zentrum Mathematik, Technische Universität München, München, Germany
Venue:
Advances in Computational Mathematics
Year:
2012

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Abstract

We provide an explicit formula for a large class of exponential B-splines. Also, we characterize the cases where the integer-translates of an exponential B-spline form a partition of unity up to a multiplicative constant. As an application of this result we construct explicitly given pairs of dual Gabor frames.