English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

We construct a one-parameter family of Laplacians on the Sierpinski Gasketthat are symmetric and self-similar for the 9-map iterated function systemobtained by iterating the standard 3-map iterated function system. Our mainresult is the fact that all these Laplacians satisfy a version of spectraldecimation that builds a precise catalog of eigenvalues and eigenfunctions forany choice of the parameter. We give a number of applications of this spectraldecimation. We also prove analogous results for fractal Laplacians on the unitInterval, and this yields an analogue of the classical Sturm-Liouville theoryfor the eigenfunctions of these one-dimensional Laplacians.

Spectral Decimation for Families of Self-Similar Symmetric Laplacians on the Sierpinski Gasket