The behaviour of the spectral counting function for a family of sets with fractal boundaries

James Fawkes

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We construct a one-parameter family of sets in R2 generated by a disjoint union of open squares. We study the spectral counting function associated to a variational Dirichlet eigenvalue problem on a set from this family and show that the spectral asymptotics depend not only on the Mmkowski dimension of the boundary, but also on whether the values of a specific function of the parameter are rational or irrational. Furthermore, we significantly sharpen the results in the rational case.

Original languageEnglish
Pages (from-to)126-138
Number of pages13
JournalJournal of the London Mathematical Society
Volume55
Issue number1
Publication statusPublished - Feb 1997

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