Self-similar Energies On Finitely Ramified Fractals

Roberto Peirone (University Of Rome Tor Vergata, Italy)

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English

World Scientific Publishing Co Pte Ltd
22 October 2025

Functional analysis & transforms; Fractal geometry

Series: Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications

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This monograph delves into 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.

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 in which copies intersect at only finitely many points. To date, a comprehensive theory for infinitely ramified fractals remains elusive.

By: Roberto Peirone (University Of Rome Tor Vergata Italy)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Volume: 9
ISBN: 9789819809141
ISBN 10: 9819809142
Series: Fractals And Dynamics In Mathematics, Science, And The Arts: Theory And Applications
Pages: 492
Publication Date: 22 October 2025
Audience: College/higher education , Professional and scholarly , Primary , Undergraduate
Format: Hardback
Publisher's Status: Forthcoming