Eigenvalue bounds and spectral asymptotics for fractal Laplacians

  • Juan Pablo Pinasco

    Universidad de Buenos Aires, Argentina
  • Cristian Scarola

    Universidad de La Pampa, Santa Rosa, Argentina
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Abstract

In this work we present Lyapunov type inequalities for generalized one dimensional Laplacian operators defined by positive atomless Borel measures. As applications, we present lower bounds for the first eigenvalue when the measure is a Bernoulli convolution, with or without overlaps. Also, for symmetric Bernoulli convolutions we obtain two sided bounds for higher eigenvalues, and we recover the asymptotic growth of the spectral counting function by elementary means without using the Renewal Theorem.

Cite this article

Juan Pablo Pinasco, Cristian Scarola, Eigenvalue bounds and spectral asymptotics for fractal Laplacians. J. Fractal Geom. 6 (2019), no. 2, pp. 109–126

DOI 10.4171/JFG/71