Basic Fourier series on a q-linear grid: Convergence theorems |
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Authors: | JL Cardoso |
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Institution: | Departamento de Matemática, Universidade de Trás-os-Montes e Alto Douro, Apartado 202, 5001-911 Vila Real, Portugal |
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Abstract: | For 0<q<1 define the symmetric q-linear operator acting on a suitable function f(x) by δf(x)=f(q1/2x)−f(q−1/2x). The q-linear initial value problem , f(0)=1, has two entire functions Cq(z) and Sq(z) as linearly independent solutions, which are orthogonal on a discrete set. Sufficient conditions for pointwise convergence and for uniform convergence of the corresponding Fourier expansion are given. |
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Keywords: | q-Trigonometric functions q-Fourier series Convergence theorems |
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