PL
 |
EN
Preferencje help
Polish version English version Język
Widoczny [Schowaj] Abstrakt
Liczba wyników

Znaleziono wyników: 4

Liczba wyników na stronie
first rewind previous Strona / 1 next fast forward last
Wyniki wyszukiwania
help Sortuj według:

help Ogranicz wyniki do:
first rewind previous Strona / 1 next fast forward last
1
Content available Operators induced by certain hypercomplex systems
Alpay Daniel, Cho Ilwoo
Opuscula Mathematica
|
2023
|
Vol. 43, no. 3
275--333
EN
In this paper, we consider a family {Ht}t∈R of rings of hypercomplex numbers, indexed by the real numbers, which contain both the quaternions and the split-quaternions. We consider natural Hilbert-space representations {(C2, πt)} t∈R of the hypercomplex system {Ht}t∈R, and study the realizations πt(h) of hypercomplex numbers h ∈ Ht, as (2 × 2)-matrices acting on C2, for an arbitrarily fixed scale t ∈ R. Algebraic, operator-theoretic, spectral-analytic, and free-probabilistic properties of them are considered.
2
Content available remote Spectral properties of certain operators on the free Hilbert space ℑ [H1, . . . , HN] and the semicircular law
Cho Ilwoo
Opuscula Mathematica
|
2021
|
Vol. 41, no. 6
755-803
EN
In this paper, we fix N -many l2-Hilbert spaces Hk whose dimensions are [formula] for k=1,…, N, for N ∈N\{1}. And then, construct a Hilbert space ℑ = ℑ [H1 , . . . , HN] induced by H1 , . . . , HN, and study certain types of operators on ℑ. In particular, we are interested in so-called jump-shift operators. The main results (i) characterize the spectral properties of these operators, and (ii) show how such operators affect the semicircular law induced by [formula], where Bk are the orthonormal bases of Hk , for k = 1, . . . , N.
3
Content available Multi-variable quaternionic spectral analysis
Cho Ilwoo, Jorgensen Palle E. T.
Opuscula Mathematica
|
2021
|
Vol. 41, no. 3
3
EN
In this paper, we consider finite dimensional vector spaces Hn over the ring H of all quaternions. In particular, we are interested in certain functions acting on Hn , and corresponding functional equations. Our main results show that (i) all quaternions of H are classified by the spectra of their realizations under representation, (ii) all vectors of Hn are classified by a canonical extended setting of (i), and (iii) the usual spectral analysis on the matricial ring Mn (C) of all (n x n)-matrices over the complex numbers C has close connections with certain “non-linear” functional equations on Hn up to the classification of (ii).
4
Content available Deformation of semicircular and circular laws via p-adic number fields and sampling of primes
Cho Ilwoo, Jorgensen Palie E. T.
Opuscula Mathematica
|
2019
|
Vol. 39, no. 6
773--813
EN
In this paper, we study semicircular elements and circular elements in a certain Banach *-probability space [formula] induced by analysis on the p-adic number fields Qp over primes p. In particular, by truncating the set P of all primes for given suitable real numbers t < s in R, two different types of truncated linear functionals [formula], and [formula] re constructed on the Banach *-algebra [formula]. We show how original free distributional data (with respect to r°) are distorted by the truncations on P (with respect to [formula], and [formula]). As application, distorted free distributions of the semicircular law, and those of the circular law are characterized up to truncation.
first rewind previous Strona / 1 next fast forward last
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.