2 papers
math.MG2025
Fractal Zeta Functions and Complex Dimensions of Ahlfors Metric Measure Spaces
Michel L. Lapidus, Sean Watson
While classical analysis dealt primarily with smooth spaces, much research has been done in the last half century on expanding the theory to the nonsmooth case. Metric Measure spac…
math-ph2024
Diffraction measures and patterns of the complex dimensions of self-similar fractal strings. I. The lattice case
Michel L. Lapidus, Machiel van Frankenhuijsen, Edward K. Voskanian
We give a generalization of Lagarias' formula for diffraction by ideal crystals, and we apply it to the lattice case, in preparation for addressing the problem of quasicrystals and…