Approximation of bandlimited functions by trigonometric polynomials |
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Authors: | S Norvidas |
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Institution: | 1. Institute of Mathematics and Informatics, Akademijos 4, Vilnius, 08663, Lithuania
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Abstract: | Let σ > 0. For 1 ≦ p ≦ ∞, the Bernstein space B σ p is a Banach space of all f ∈ L p (?) such that f is bandlimited to σ; that is, the distributional Fourier transform of f is supported in ?σ,σ]. We study the approximation of f ∈ B σ p by finite trigonometric sums $$ P_\tau (x) = \chi _\tau (x) \cdot \sum\limits_{|k| \leqq \sigma \tau /\pi } {c_{k,\tau } e^{i\frac{\pi } {\tau }kx} } $$ in L p norm on ? as τ → ∞, where χ τ denotes the indicator function of ?τ, τ]. |
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