منابع مشابه
Interlacing property for B-splines
We prove that the zeros of the derivatives of any order of a B-spline are increasing functions of its interior knots. We then prove that if the interior knots of two Bsplines interlace, then the zeros of their derivatives of any order also interlace. The same results are obtained for Chebyshevian B-splines.
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We provide an explicit formula for a large class of exponential Bsplines. 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.
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A new type of B-spline the expo-rational B-spline is introduced. The heuristic motivation for its introduction comes from important similarities in several celebrated mathematical constructions originating in approximation theory, differential geometry and operator theory. The main result of the paper is the derivation of an Edgeworth and a steepest-descent/saddlepoint asymptotic expansion whic...
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ژورنال
عنوان ژورنال: Journal of Approximation Theory
سال: 2005
ISSN: 0021-9045
DOI: 10.1016/j.jat.2005.03.001