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Lacunary series in weighted spaces of analytic functions
Archiv der Mathematik, 2011Following \textit{A. L. Shields} and \textit{D. L. Williams} [Trans. Am. Math. Soc. 162(1971), 287--302 (1972; Zbl 0227.46034)], a positive function \(\psi\) defined on \([1,\infty)\) is said to be normal if there exist positive constants \(\alpha\) and \(\beta\) such that \(\psi(t)/t^\alpha\) is non-decreasing and \(\psi(t)/t^\beta\) is non-increasing
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Müntz-Szasz Theorems and Lacunary Entire Functions
1978This lecture discusses the case of non-completeness for the Muntz-Szasz theorem and Malliavin’s theorem. Various applications to entire functions with gaps are presented.
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Lacunary Measures and Self–similar Probability Measures in Function Spaces
Acta Mathematica Sinica, English Series, 2004Let \(\mu\) be a Radon measure with bounded support of Lebesgue measure zero. In multifractal geometry, one consideres the quantity \[ \mu^\lambda_{p,q}= \biggl(\sum_j 2^{j\lambda q} \biggl(\sum_m \mu(Q_{j,m})^p\biggr)^{q/p}\biggr)^{1/q}, \] \(\lambda\in {\mathbb R}\) and \(Q_{j,m}\) denotes a standard dyadic cube. Let \(t=\frac 1 p\) and \(\lambda_\mu(
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Lacunary statistical boundedness of measurable functions
Mathematics in Natural Science, 2020openaire +1 more source
Lacunary subsystems of the Walsh system of functions
Siberian Mathematical Journal, 1979openaire +1 more source