85 citations · 341 across the 49 of their papers we have counts for
51 papers
Distributional Fractional Taylor Series and Interpretation of the Fractal and Number-Theoretic Explicit Formulas
Michel L. Lapidus, Matthew Overduin
Motivated by the work of M. L. Lapidus and M. van Frankenhuisjen on fractal explicit formulas for generalized fractal strings, we develop in this paper a distributional fractal Tay…
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…
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…
-adic fractal strings of arbitrary rational dimensions and Cantor strings
Michel L. Lapidus, Hùng Lũ', Machiel van Frankenhuijsen
The local theory of complex dimensions for real and -adic fractal strings describes oscillations that are intrinsic to the geometry, dynamics and spectrum of archimedean and non…
Metric Approximations of Spectral Triples on the Sierpiński Gasket and other fractal curves
Therese-Marie Landry, Michel L. Lapidus, Frederic Latremoliere
Noncommutative geometry provides a framework, via the construction of spectral triples, for the study of the geometry of certain classes of fractals. Many fractals are constructed…
Quasiperiodic patterns of the complex dimensions of nonlattice self-similar strings, via the LLL algorithm
Michel L. Lapidus, Machiel van Frankenhuijsen, Edward K. Voskanian
The Lattice String Approximation algorithm (or LSA algorithm) of M. L. Lapidus and M. van Frankenhuijsen is a procedure that approximates the complex dimensions of a nonlattice sel…