The limited Rademacher functions and Bernoulli convolutions associated with Pisot numbers
By De-Jun Feng. 2005
91 citations recorded by the source corpus.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/2b5c1dfa376045c7677c243054d303a1b1000b80
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In Condensed Matter Physics
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Quantization (2019, unknown): “Combining the results in [18] and those in [7, 19, 22], one can obtain explicit formulas for the quantization dimension for a large class of self-similar measures with overlaps.”
- Multifractal analysis of weak Gibbs measures and phase transition—application to some Bernoulli convolutions (2003, background): “In [13], the first author completes a result in [24] by giving an explicit formula for the L -spectrum of the Erdös measure, proving in addition that there exists a negative qc such that: (i) τ (q) = q log 2/logβ for any q ≤ qc; (ii) τ is infinitely differentiable at any q > qc; and (iii) τ is not d”
- Lyapunov exponents for products of matrices and multifractal analysis. Part II: General matrices (2003, background): “The structure of this measure has been extensively studied in [13].”
- A Class of Self-Affine Sets and Self-Affine Measures (2005, background): “For a self-similar measure without the open set condition, however, the Lq spectrum is generally difficult to obtain and is calculated for only a few special cases, see [18, 7, 8 , 19].”
- Non-spectral problem for a class of planar self-affine measures (2008, background): “Previous research on such measure and its Fourier transform revealed some surprising connections with a number of areas in mathematics, such as harmonic analysis, dynamical systems, number theory, and others, see [8,9,20,30,31] and references cited therein.”
- Multifractal formalism for self-similar measures with weak separation condition (2009, background): “MSC: 28A78; 28A80 Keywords: Self-similar measures; Multifractal formalism; Weak separation condition; Moran structure”
- The thermodynamic formalism for sub-additive potentials (2007, background): “It is known that in many interesting cases a self-similar measure with overlaps can be locally represented as infinite products of a family of matrices (see, e.g., [12, 15 , 19, 20]).”
- Dimension theory of iterated function systems (2009, methodology): “[16, 17, 36, 39, 37]), and furthermore the Hausdorff dimension ofK can be computed (see e.”