Zobrazeno 1 - 10
of 774
pro vyhledávání: '"LAPIDUS, A. L."'
Publikováno v:
Houston Journal of Mathematics, Volume 49, Number 4, 2023, Pages 833-859
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 complex dimensions posed by Lapidus and van Frankenhuijsen concerning
Externí odkaz:
http://arxiv.org/abs/2305.09050
The local theory of complex dimensions for real and $p$-adic fractal strings describes oscillations that are intrinsic to the geometry, dynamics and spectrum of archimedean and nonarchimedean fractal strings. We aim to develop a global theory of comp
Externí odkaz:
http://arxiv.org/abs/2012.11535
Publikováno v:
Adv. Math. 385 (2021), Paper No. 107771, 43 pp
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 as natural limits of certain sets with a simpler structure: for instan
Externí odkaz:
http://arxiv.org/abs/2010.06921
Publikováno v:
Mathematics No. 9, 6 (2021), 591
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 self-similar fractal string by the complex dimensions of a lattice self-s
Externí odkaz:
http://arxiv.org/abs/2009.03493
Akademický článek
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Publikováno v:
Pure and Applied Functional Analysis, Volume 5, Number 5, 1073-1094, 2020
We study the essential singularities of geometric zeta functions $\zeta_{\mathcal L}$, associated with bounded fractal strings $\mathcal L$. For any three prescribed real numbers $D_{\infty}$, $D_1$ and $D$ in $[0,1]$, such that $D_{\infty}
Externí odkaz:
http://arxiv.org/abs/1908.07845
Autor:
Lapidus, Michel L.
Our main goal in this long survey article is to provide an overview of the theory of complex fractal dimensions and of the associated geometric or fractal zeta functions, first in the case of fractal strings (one-dimensional drums with fractal bounda
Externí odkaz:
http://arxiv.org/abs/1803.10399
Publikováno v:
In Mendeleev Communications November-December 2022 32(6):804-806
Autor:
Cobler, Tim, Lapidus, Michel L.
Emil Artin defined a zeta function for algebraic curves over finite fields and made a conjecture about them analogous to the famous Riemann hypothesis. This and other conjectures about these zeta functions would come to be called the Weil conjectures
Externí odkaz:
http://arxiv.org/abs/1705.06222
Akademický článek
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