Fourier Series with Linear Splines on an Interval |
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| Authors: | Daniela Roşca |
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| Institution: | (1) Université catholique de Louvain, 2 chemin du Cyclotron, B-1348 Louvain-la-Neuve, Belgium;(2) Department of Mathematics, Technical University of Cluj-Napoca, str. Daicoviciu 15, RO-400 020 Cluj-Napoca, Romania |
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| Abstract: | We construct orthonormal bases of linear splines on a finite interval a, b] and then we study the Fourier series associated to these orthonormal bases. For continuous functions defined on a, b], we prove that the associated Fourier series converges pointwisely on (a, b) and also uniformly on a, b], if it convergences pointwisely at a and b. |
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| Keywords: | 42A65 42A20 41A15 |
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