Browsing by Subject "p-adic number fields"

Now showing 1 - 3 of 3

Access status: Open Access ,
Adelic analysis and functional analysis on the finite Adele ring
(Wydawnictwa AGH, 2018) Cho, Ilwoo
In this paper, we study operator theory on the $∗$-algebra $\mathcal{M}_{\mathcal{P}}$, consisting of all measurable functions on the finite Adele ring $A_{\mathbb{Q}}$, in extended free-probabilistic sense. Even though our $∗$-algebra $\mathcal{M}_{\mathcal{P}}$ is commutative, our Adelic-analytic data and properties on $\mathcal{M}_{\mathcal{P}}$ are understood as certain free-probabilistic results under enlarged sense of (noncommutative) free probability theory (well-covering commutative cases). From our free-probabilistic model on $A_{\mathbb{Q}}$, we construct the suitable Hilbert-space representation, and study a $C∗$-algebra $M_{\mathcal{P}}$ generated by $\mathcal{M}_{\mathcal{P}}$ under representation. In particular, we focus on operator-theoretic properties of certain generating operators on $M_{\mathcal{P}}$.
Access status: Open Access ,
Deformation of semicircular and circular laws via p-adic number fields and sampling of primes
(Wydawnictwa AGH, 2019) Cho, Ilwoo; Jørgensen, Palle E.T.
In this paper, we study semicircular elements and circular elements in a certain Banach $∗$-probability space $(\mathfrak{LS},\tau ^{0})$ induced by analysis on the $p$-adic number fields $\mathbb{Q}_{p}$ over primes $p$. In particular, by truncating the set $\mathcal{P}$ of all primes for given suitable real numbers $t\lt s$ in $\mathbb{R}$, two different types of truncated linear functionals $\tau_{t_{1}\lt t_{2}}$, and $\tau_{t_{1}\lt t_{2}}^{+}$ are constructed on the Banach $∗$-algebra $(\mathfrak{LS}$. We show how original free distributional data (with respect to $\tau ^{0}$) are distorted by the truncations on $\mathcal{p}$ (with respect to $\tau_{t\lt s}$, and $\tau_{t\lt s}^{+}$). As application, distorted free distributions of the semicircular law, and those of the circular law are characterized up to truncation.
Access status: Open Access ,
On dynamical systems induced by p-adic number fields
(2015) Cho, Ilwoo
In this paper, we construct dynamical systems induced by $p$-adic number fields $\mathbb{Q}_{p}$. We study the corresponding crossed product operator algebras induced by such dynamical systems. In particular, we are interested in structure theorems, and free distributional data of elements in the operator algebras.