Roberto Peirone

Self-Similar Energies on Finitely Ramified Fractals

Sprache: Englisch.
gebunden , 420 Seiten
ISBN 9819809142
EAN 9789819809141
Veröffentlicht 30. September 2025
Verlag/Hersteller World Scientific Publishing Company
144,50 inkl. MwSt.
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Beschreibung

Analysis on fractals began to take shape as a mathematical field in the late 1980s. Traditionally, the focus of analysis has been on finitely ramified fractals -- those where copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive.This monograph outlines the theory of self-similar energies on finitely ramified self-similar fractals. Using these self-similar energies, one can construct Laplacians, harmonic functions, Brownian motion, and differential equations specific to these fractals.On finitely ramified fractals, self-similar energies are derived from eigenforms -- quadratic forms that are eigenvectors of a special nonlinear operator within a finite-dimensional function space. The monograph also explores conditions for the existence and uniqueness of these self-similar energies and addresses related problems. For certain cases, complete solutions are provided.

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