Zobrazeno 1 - 10
of 101
pro vyhledávání: '"Balka, Richárd"'
Spectral properties of bounded linear operators play a crucial role in several areas of mathematics and physics. For each self-adjoint, trace-class operator $O$ we define a set $\Lambda_n\subset \mathbb{R}$, and we show that it converges to the spect
Externí odkaz:
http://arxiv.org/abs/2407.04478
Positivity preservation is an important issue in the dynamics of open quantum systems: positivity violations always mark the border of validity of the model. We investigate the positivity of self-adjoint polynomial Gaussian integral operators $\wideh
Externí odkaz:
http://arxiv.org/abs/2405.04438
Autor:
Balka, Richárd, Keleti, Tamás
We introduce a new family of fractal dimensions by restricting the set of diameters in the coverings in the usual definition of the Hausdorff dimension. Among others, we prove that this family contains continuum many distinct dimensions, and they sha
Externí odkaz:
http://arxiv.org/abs/2312.06456
Autor:
Balka, Richárd, Keleti, Tamás
We consider the question which compact metric spaces can be obtained as a Lipschitz image of the middle third Cantor set, or more generally, as a Lipschitz image of a subset of a given compact metric space. In the general case we prove that if $A$ an
Externí odkaz:
http://arxiv.org/abs/2308.02639
We say that $E$ is a microset of the compact set $K\subset \mathbb{R}^d$ if there exist sequences $\lambda_n\geq 1$ and $u_n\in \mathbb{R}^d$ such that $(\lambda_n K + u_n ) \cap [0,1]^d$ converges to $E$ in the Hausdorff metric, and moreover, $E \ca
Externí odkaz:
http://arxiv.org/abs/2102.13059
Publikováno v:
Proc. Amer. Math. Soc. 150 (2022) 3889-3898
The lower dimension $\dim_L$ is the dual concept of the Assouad dimension. As it fails to be monotonic, Fraser and Yu introduced the modified lower dimension $\dim_{ML}$ by making the lower dimension monotonic with the simple formula $\dim_{ML} X=\su
Externí odkaz:
http://arxiv.org/abs/2102.13049
Publikováno v:
Adv. Math. 385 (2021) 107773
S. Banach pointed out that the graph of the generic (in the sense of Baire category) element of $\text{Homeo}([0,1])$ has length $2$. J. Mycielski asked if the measure theoretic dual holds, i.e., if the graph of all but Haar null many (in the sense o
Externí odkaz:
http://arxiv.org/abs/2009.14106
We answer a question of Banakh, Jab\l{}o\'nska and Jab\l{}o\'nski by showing that for $d\ge 2$ there exists a compact set $K \subseteq \mathbb{R}^d$ such that the projection of $K$ onto each hyperplane is of non-empty interior, but $K+K$ is nowhere d
Externí odkaz:
http://arxiv.org/abs/2006.15206
Autor:
Balka, Richárd
Let $X=\{(X_1(t),\dots,X_d(t)): t\in \mathbb{R}^n\}$ be a Gaussian random field in $\mathbb{R}^d$ such that $X_1,\dots,X_d$ are independent, centered Gaussian random fields with continuous sample paths. Let $f\colon \mathbb{R}^n\to \mathbb{R}^d$ be a
Externí odkaz:
http://arxiv.org/abs/1610.06474