Self-similar Energies On Finitely Ramified Fractals (eBook)

Peirone Roberto Peirone (Autor)

eBook Download: PDF

2025
492 Seiten
World Scientific Publishing Company (Verlag)
978-981-98-0915-8 (ISBN)

Infos

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.

Produkt-Details

• Erscheint lt. Verlag: 19.9.2025
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
• ISBN-10: 981-98-0915-0 / 9819809150
• ISBN-13: 978-981-98-0915-8 / 9789819809158