Open Access. Powered by Scholars. Published by Universities.®
Articles 1 - 6 of 6
Full-Text Articles in Mathematics
Thin Sequences And The Gram Matrix, Pamela Gorkin, John E. Mccarthy, Sandra Pott, Brett D. Wick
Thin Sequences And The Gram Matrix, Pamela Gorkin, John E. Mccarthy, Sandra Pott, Brett D. Wick
Mathematics Faculty Publications
We provide a new proof of Volberg’s Theorem characterizing thin interpolating sequences as those for which the Gram matrix associated to the normalized reproducing kernels is a compact perturbation of the identity. In the same paper, Volberg characterized sequences for which the Gram matrix is a compact perturbation of a unitary as well as those for which the Gram matrix is a Schatten-2 class perturbation of a unitary operator. We extend this characterization from 2 to p, where 2 p ≤∞.
Hankel Vector Moment Sequences And The Non-Tangential Regularity At Infinity Of Two Variable Pick Functions, Jim Agler, John E. Mccarthy
Hankel Vector Moment Sequences And The Non-Tangential Regularity At Infinity Of Two Variable Pick Functions, Jim Agler, John E. Mccarthy
Mathematics Faculty Publications
A Pick function of variables is a holomorphic map from to , where is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series with real numbers that gives an asymptotic expansion on non-tangential approach regions to infinity. In 1921 H. Hamburger characterized which sequences can occur. We give an extension of Hamburger's results to Pick functions of two variables.
Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, N J. Young
Operator Monotone Functions And Löwner Functions Of Several Variables, Jim Agler, John E. Mccarthy, N J. Young
Mathematics Faculty Publications
We prove generalizations of Loewner's results on matrix monotone functions to several variables. We give a characterization of when a function of d variables is locally monotone on d-tuples of commuting self-adjoint n-by-n matrices. We prove a generalization to several variables of Nevanlinna's theorem describing analytic functions that map the upper half-plane to itself and satisfy a growth condition. We use this to characterize all rational functions of two variables that are operator monotone.
A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh
A New Undergraduate Curriculum On Mathematical Biology At University Of Dayton, Muhammad Usman, Amit Singh
Mathematics Faculty Publications
The beginning of modern science is marked by efforts of pioneers to understand the natural world using a quantitative approach. As Galileo wrote, "the book of nature is written in the language of mathematics". The traditional undergraduate course curriculum is heavily focused on individual disciplines like biology, physics, chemistry, mathematics rather than interdisciplinary courses. This fragmented teaching of sciences in majority of universities leave biology outside the quantitative and mathematical approaches. The landscape of biomedical science has transformed dramatically with advances in high throughput experimental approaches, which led to the huge amount of data. The best possible approach to generate …
On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth
On T-Pure And Almost Pure Exact Sequences Of Lca Groups, Peter Loth
Mathematics Faculty Publications
A proper short exact sequence in the category of locally compact abelian groups is said to be t-pure if φ(A) is a topologically pure subgroup of B, that is, if for all positive integers n. We establish conditions under which t-pure exact sequences split and determine those locally compact abelian groups K ⊕ D (where K is compactly generated and D is discrete) which are t-pure injective or t-pure projective. Calling the extension (*) almost pure if for all positive integers n, we obtain a complete description of the almost pure injectives and almost pure projectives in the category of …
The Duals Of Warfield Groups, Peter Loth
The Duals Of Warfield Groups, Peter Loth
Mathematics Faculty Publications
A Warfield group is a direct summand of a simply presented abelian group. In this paper, we describe the Pontrjagin dual groups of Warfield groups, both for the p-local and the general case. A variety of characterizations of these dual groups is obtained. In addition, numerical invariants are given that distinguish between two such groups which are not topologically isomorphic.