Zobrazeno 1 - 10
of 126
pro vyhledávání: '"Grabner, Peter J."'
We extend the notion of hyperuniformity to the projective spaces $\mathbb{RP}^{d-1}$, $\mathbb{CP}^{d-1}$, $\mathbb{HP}^{d-1}$, and $\mathbb{OP}^2$. We show that hyperuniformity implies uniform distribution and present examples of deterministic point
Externí odkaz:
http://arxiv.org/abs/2403.03572
Spherical needlets were introduced by Narcowich, Petrushev, and Ward to provide a multiresolution sequence of polynomial approximations to functions on the sphere. The needlet construction makes use of integration rules that are exact for polynomials
Externí odkaz:
http://arxiv.org/abs/2207.12838
In this paper we study Riesz, Green and logarithmic energy on two-point homogeneous spaces. More precisely we consider the real, the complex, the quaternionic and the Cayley projective spaces. For each of these spaces we provide upper estimates for t
Externí odkaz:
http://arxiv.org/abs/2204.04015
Publikováno v:
In Applied and Computational Harmonic Analysis November 2024 73
We study integrals of the form \begin{equation*} \int_{-1}^1(C_n^{(\lambda)}(x))^2(1-x)^\alpha (1+x)^\beta\, dx, \end{equation*} where $C_n^{(\lambda)}$ denotes the Gegenbauer-polynomial of index $\lambda>0$ and $\alpha,\beta>-1$. We give exact formu
Externí odkaz:
http://arxiv.org/abs/2103.08303
Autor:
Grabner, Peter J.
Publikováno v:
The Ramanujan Journal 2021
Extremal quasimodular forms have been introduced by M.~Kaneko and M.Koike as as quasimodular forms which have maximal possible order of vanishing at $i\infty$. We show an asymptotic formula for the Fourier coefficients of such forms. This formula is
Externí odkaz:
http://arxiv.org/abs/2007.13569
Autor:
Grabner, Peter J.
Publikováno v:
International Journal of Number Theory 16 (2020)
We study quasimodular forms of depth $\leq4$ and determine under which conditions they occur as solutions of modular differential equations. Furthermore, we study which modular differential equations have quasimodular solutions. We use these results
Externí odkaz:
http://arxiv.org/abs/2002.02736
Autor:
Grabner, Peter J.
Publikováno v:
Indagationes Mathematicae 2022
We study measures that are obtained as push-forwards of measures of maximal entropy on sofic shifts under digital maps $(x_k)_{k\in\mathbb{N}}\mapsto\sum_{k\in\mathbb{N}}x_k\beta^{-k}$, where $\beta>1$ is a Pisot number. We characterise the continuit
Externí odkaz:
http://arxiv.org/abs/1908.09023
Publikováno v:
Math. Proc. Camb. Phil. Soc. 171 (2021) 329-367
We give a unified description of the modular and quasi-modular functions used in Viazovska's proof of the best packing bounds in dimension 8 and the proof by Cohn, Kumar, Miller, Radchenko, and Viazovska of the best packing bound in dimension 24. We
Externí odkaz:
http://arxiv.org/abs/1907.08558
We define a notion of Poissonian pair correlation (PPC) for Riemannian manifolds without boundary and prove that PPC implies uniform distribution in this setting. This extends earlier work by Grepstad and Larcher, Aistleitner, Lachmann, and Pausinger
Externí odkaz:
http://arxiv.org/abs/1904.08286