Opuscula Mathematica
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ISSN 1232-9274
e-ISSN: 2300-6919
Issue Date
2018
Volume
Vol. 38
Number
No. 4
Description
Journal Volume
Opuscula Mathematica
Vol. 38 (2018)
Projects
Pages
Articles
Positive definite functions and dual pairs of locally convex spaces
(Wydawnictwa AGH, 2018) Alpay, Daniel; Gabrielân, Saak Sarkisovič
Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive definite functions.
On spectra of quadratic operator pencils with rank one gyroscopic linear part
(Wydawnictwa AGH, 2018) Bojko, Olga Pavlìvna; Martinûk, Olʹga Mikolaïvna; Pivovarčik, Vâčeslav
The spectrum of a selfadjoint quadratic operator pencil of the form $\lambda^2M-\lambda G-A$ is investigated where $M\geq 0$, $G\geq 0$ are bounded operators and $A$ is selfadjoint bounded below is investigated. It is shown that in the case of rank one operator $G$ the eigenvalues of such a pencil are of two types. The eigenvalues of one of these types are independent of the operator $G$. Location of the eigenvalues of both types is described. Examples for the case of the Sturm-Liouville operators $A$ are given.
Banach *-algebras generated by semicircular elements induced by certain orthogonal projections
(Wydawnictwa AGH, 2018) Cho, Ilwoo; Jørgensen, Palle E.T.
The main purpose of this paper is to study structure theorems of Banach $∗$-algebras generated by semicircular elements. In particular, we are interested in the cases where given semicircular elements are induced by orthogonal projections in a $C^{*}$-probability space.
On the non-existence of zero modes
(Wydawnictwa AGH, 2018) Elton, Daniel M.
We consider magnetic fields on $\mathbb{R}^3$ which are parallel to a conformal Killing field. When the latter generates a simple rotation we show that a Weyl-Dirac operator with such a magnetic field cannot have a zero mode. In particular this allows us to expand the class of non zero mode producing magnetic fields to include examples of non-trivial smooth compactly supported fields.
Linear Sturm-Liouville problems with Riemann-Stieltjes integral boundary conditions
(Wydawnictwa AGH, 2018) Kong, Qingkai; George, Thomas E. St.
We study second-order linear Sturm-Liouville problems involving general homogeneous linear Riemann-Stieltjes integral boundary conditions. Conditions are obtained for the existence of a sequence of positive eigenvalues with consecutive zero counts of the eigenfunctions. Additionally, we find interlacing relationships between the eigenvalues of such Sturm-Liouville problems and those of Sturm-Liouville problems with certain two-point separated boundary conditions.