Convergence of mock Fourier series on generalized Bernoulli convolutions. (English) Zbl 1497.42006
Summary: We investigate the problem of convergence of a class of trigonometric series supported on the generalized Bernoulli convolutions \(\mu\) on \(\mathbb{R} \). Our main result shows that, under a technical condition, there are continuum many exponential orthonormal bases for \(L^2(\mu )\) such that the associated mock Fourier series converge to itself in the sense of uniform, \(L^p\) \((1\leq p\leq \infty )\)-norm and \(\mu \)-almost pointwise.
MSC:
| 42A20 | Convergence and absolute convergence of Fourier and trigonometric series |
| 42B25 | Maximal functions, Littlewood-Paley theory |
| 28A80 | Fractals |
| 42A38 | Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type |
Keywords:
mock Fourier series; mock Fourier transform; spectral measures; Dirichlet kernel; Hardy-Littlewood maximal operator; generalized Bernoulli convolutionsReferences:
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