On spectra and spectral eigenmatrix problems of the planar Sierpinski measures

DOI10.1512/iumj.2022.71.8873zbMath1487.42060OpenAlexW4285117893MaRDI QIDQ5075684

Xing-Gang He, Li-Xiang An, Xin-Han Dong

Publication date: 11 May 2022

Published in: Indiana University Mathematics Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1512/iumj.2022.71.8873

zbMATH Keywords

spectral measuresSierpinski measuresspectral structuresFourier orthogonal familyspectral eigenmatrix problems

Mathematics Subject Classification ID

Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Fourier series in special orthogonal functions (Legendre polynomials, Walsh functions, etc.) (42C10) Probabilistic measure theory (60A10) Fractals (28A80) Convolution, factorization for one variable harmonic analysis (42A85) Completeness of sets of functions in one variable harmonic analysis (42A65)

Related Items (7)

The exact number of orthogonal exponentials on the spatial Sierpinski gasket ⋮ Spectral structure of planar self-similar measures with four-element digit set ⋮ The spectral eigenmatrix problems of planar self-affine measures with four digits ⋮ Spectral eigenmatrix of the planar spectral measures with four elements ⋮ On spectra and spectral eigenmatrices of self-affine measures on \(\mathbb{R}^n\) ⋮ On the quasi-Beurling dimensions of the spectra for planar Moran-type Sierpinski spectral measures ⋮ On spectral structure and spectral eigenvalue problems for a class of self similar spectral measure with product form

Cites Work

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• Cauchy transforms of self-similar measures: Starlikeness and univalence
• Cauchy Transforms of Self-Similar Measures
• An Integral Related to the Cauchy Transform on the Sierpinski Gasket
• Fourier series on fractals: a parallel with wavelet theory
• Fourier Analysis and Hausdorff Dimension
• Divergence of the mock and scrambled Fourier series on fractal measures

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