Publicação
Basic Fourier series on a q-linear grid: convergence theorems
| Resumo: | For 0 < q < 1 define the symmetric q-linear operator acting on a suitable function f (x) by δf (x) = (f (q^{1/2}x) − f (q^{−1/2}x). The q-linear initial value problem δf (x)/δx = λf (x), f (0) = 1, has two entire functions C_q(z) and S_q(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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| Autores principais: | Cardoso, J. L. |
| Assunto: | q-Trigonometric functions q-Fourier series Convergence theorems |
| Ano: | 2006 |
| País: | Portugal |
| Tipo de documento: | artigo |
| Tipo de acesso: | acesso restrito |
| Instituição associada: | Universidade de Trás-os-Montes e Alto Douro |
| Idioma: | inglês |
| Origem: | Repositório da UTAD |
| Resumo: | For 0 < q < 1 define the symmetric q-linear operator acting on a suitable function f (x) by δf (x) = (f (q^{1/2}x) − f (q^{−1/2}x). The q-linear initial value problem δf (x)/δx = λf (x), f (0) = 1, has two entire functions C_q(z) and S_q(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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