Spectral analysis of Laplacians on the Vicsek set

• Autores: Denglin Zhou
• Localización: Pacific journal of mathematics, ISSN 0030-8730, Vol. 241, Nº 2, 2009, págs. 369-398
• Idioma: inglés
• DOI: 10.2140/pjm.2009.241.369
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• Resumen

  • We find the spectral decimation function for the standard Laplacian on the symmetric Vicsek set, expressed in terms of Chebyshev polynomials. This allows us to determine the order of the eigenvalues of the Laplacian, describe their asymptotic behavior and prove that there exist gaps in the spectrum.