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1. CMB 2011 (vol 55 pp. 487)
Weighted Model Sets and their Higher Point-Correlations Examples of distinct weighted model sets with equal $2,3,4, 5$-point
correlations are given.
Keywords:model sets, correlations, diffraction Categories:52C23, 51P05, 74E15, 60G55 |
2. CMB 2011 (vol 55 pp. 339)
From Matrix to Operator Inequalities We generalize LÃ¶wner's method for proving that matrix monotone
functions are operator monotone. The relation $x\leq y$ on bounded
operators is our model for a definition of $C^{*}$-relations
being residually finite dimensional.
Our main result is a meta-theorem about theorems involving relations
on bounded operators. If we can show there are residually finite dimensional
relations involved and verify a technical condition, then such a
theorem will follow from its restriction to matrices.
Applications are shown regarding norms of exponentials, the norms
of commutators, and "positive" noncommutative $*$-polynomials.
Keywords:$C*$-algebras, matrices, bounded operators, relations, operator norm, order, commutator, exponential, residually finite dimensional Categories:46L05, 47B99 |
3. CMB 2011 (vol 54 pp. 487)
Some Properties Associated with Adequate Transversals In this paper, another relationship between the quasi-ideal adequate transversals
of an abundant semigroup is given. We introduce the concept of a weakly multiplicative
adequate transversal and the classic result that an adequate transversal is multiplicative
if and only if it is weakly multiplicative and a quasi-ideal is obtained.
Also, we give two equivalent conditions for an adequate transversal to be weakly
multiplicative. We then consider the case when $I$ and $\Lambda$ (defined below) are
bands. This is analogous to the inverse transversal if the regularity condition is adjoined.
Keywords:abundant semigroup, adequate transversal, Green's $*$-relations, quasi-ideal Category:20M10 |
4. CMB 2009 (vol 52 pp. 95)
Matrix Valued Orthogonal Polynomials on the Unit Circle: Some Extensions of the Classical Theory In the work presented below the classical subject of orthogonal
polynomials on the unit
circle is discussed in the matrix setting. An explicit matrix
representation of the matrix valued orthogonal polynomials in terms of
the moments of the measure is presented. Classical recurrence
relations are revisited using the matrix representation of the
polynomials. The matrix expressions for the kernel polynomials and the
Christoffel--Darboux formulas are presented for the first time.
Keywords:Matrix valued orthogonal polynomials, unit circle, Schur complements, recurrence relations, kernel polynomials, Christoffel-Darboux Category:42C99 |