Lacunary Interpolation by Antiperiodic Trigonometric Polynomials |
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Authors: | Franz-Jürgen Delvos Ludger Knoche |
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Institution: | (1) Lehrstuhl für Mathematik I, Universität Siegen, 57068, Siegen, Germany, email: delvos@mathematik.uni-siegen.de |
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Abstract: | The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial T exist which satisfies T(x
k) = a
k, D
m
T(x
k) = b
k, 0 k n – 1, where x
k = k/n is a nodal set, a
k and b
k are prescribed complex numbers,
and m N. Results obtained by several authors for the periodic case are extended to the antiperiodic case. In particular solvability is established when n as well as m are even. In this case a periodic solution does not exist. |
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Keywords: | Lacunary interpolation trigonometric interpolation antiperiodic trigonometric interpolation |
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