3 papers
math-ph2025
On Complex Dimensions and Heat Content of Self-Similar Fractals
William E. Hoffer, Michel L. Lapidus
Complex fractal dimensions, defined as poles of appropriate fractal zeta functions, describe the geometric oscillations in fractal sets. In this work, we show that the same possibl…
math-ph2025
Shape and Spectrum: On the Heat and Volume of Self-Similar Fractals
William Hoffer
In this work, we examine the relationship between geometry and spectrum of regions with fractal boundary. The relationship is well-understood for fractal harps in one dimension, bu…
math-ph2024
Tube Formulae for Generalized von Koch Fractals through Scaling Functional Equations
Will Hoffer
In this work, we provide a treatment of scaling functional equations in a general setting involving fractals arising from sufficiently nice self-similar systems in order to analyze…