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pro vyhledávání: '"Keßeböhmer, Marc"'
For H\"older continuous functions $f_i$, $i=0,\ldots ,d$, on a subshift of finite type and $\Theta\subset \mathbb \R^d$ we consider a parametrized family of potentials $\{F_\theta= f_0+\sum_{i=1}^d \theta_i f_i : \theta\in \Theta\}$. We show that the
Externí odkaz:
http://arxiv.org/abs/2408.01104
Autor:
Kesseböhmer, Marc, Niemann, Aljoscha
In this note, we investigate the possibility of defining meaningful upper and lower quantization dimensions for a compactly supported Borel probability measure of order $r$, also for negative values of $r$. To this end, we utilize the concept of part
Externí odkaz:
http://arxiv.org/abs/2405.13387
In the framework of infinite ergodic theory, we derive equidistribution results for suitable weighted sequences of cusp points of Hecke triangle groups encoded by group elements of constant word length with respect to a set of natural generators. Thi
Externí odkaz:
http://arxiv.org/abs/2402.04784
Autor:
Kesseböhmer, Marc, Niemann, Aljoscha
In this note, we present an abstract approach to study asymptotic orders for adaptive approximations with respect to a monotone set function $\mathfrak{J}$ defined on dyadic cubes. We determine the exact upper order in terms of the critical value of
Externí odkaz:
http://arxiv.org/abs/2312.16644
Autor:
Kesseböhmer, Marc, Wiegmann, Linus
In this paper we completely solve the problem of finding the (upper) approximation order with respect to the Kolmogorov, Gel'fand, and linear widths for the embedding of the Sobolev spaces $W^{\alpha,p}$ and $W_{0}^{\alpha,p}$ in the euclidian measur
Externí odkaz:
http://arxiv.org/abs/2303.01320
Publikováno v:
Trans. Amer. Math. Soc. 376 (2023), no. 7, 4661-4678
We provide a complete picture of the upper quantization dimension in terms of the R\'enyi dimension by proving that the upper quantization dimension $\bar{D}_{r}(\nu)$ of order $r>0$ for an arbitrary compactly supported Borel probability measure $\nu
Externí odkaz:
http://arxiv.org/abs/2205.15776
Autor:
Kesseböhmer, Marc, Niemann, Aljoscha
We study the spectral dimensions of Krein-Feller operators for arbitrary for arbitrary finite Borel measures $\nu$ on the $d$-dimensional unit cube ($d\geq2$) via a form approach. We make use of the spectral partition function of $\nu$ as introduced
Externí odkaz:
http://arxiv.org/abs/2202.05247
Cortical networks exhibit synchronized activity which often occurs in spontaneous events in the form of spike avalanches. Since synchronization has been causally linked to central aspects of brain function such as selective signal processing and inte
Externí odkaz:
http://arxiv.org/abs/2202.02520
Autor:
Kesseböhmer, Marc, Niemann, Aljoscha
Publikováno v:
J. Funct. Anal. 283 (2022), no. 7, Paper No. 109598, 22 pp
We establish a connection between the $L^{q}$-spectrum of a Borel measure $\nu $ on the $m$-dimensional unit cube and the approximation order of Kolmogorov diameters of the unit sphere with respect to Sobolev norms in $L_{\nu }^{p}$. This leads to im
Externí odkaz:
http://arxiv.org/abs/2107.07932