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Articles 1 - 6 of 6
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Partial Orders On Partial Isometries, William T. Ross, Stephan Ramon Garcia, Robert T. W. Martin
Partial Orders On Partial Isometries, William T. Ross, Stephan Ramon Garcia, Robert T. W. Martin
Department of Math & Statistics Faculty Publications
This paper studies three natural pre-orders of increasing generality on the set of all completely non-unitary partial isometries with equal defect indices. We show that the problem of determining when one partial isometry is less than another with respect to these pre-orders is equivalent to the existence of a bounded (or isometric) multiplier between two natural reproducing kernel Hilbert spaces of analytic functions. For large classes of partial isometries these spaces can be realized as the well-known model subspaces and deBranges-Rovnyak spaces. This characterization is applied to investigate properties of these pre-orders and the equivalence classes they generate.
Weak Parallelogram Laws On Banach Spaces And Applications To Prediction, William T. Ross, R. Cheng
Weak Parallelogram Laws On Banach Spaces And Applications To Prediction, William T. Ross, R. Cheng
Department of Math & Statistics Faculty Publications
This paper concerns a family of weak parallelogram laws for Banach spaces. It is shown that the familiar Lebesgue spaces satisfy a range of these inequalities. Connections are made to basic geometric ideas, such as smoothness, convexity, and Pythagorean-type theorems. The results are applied to the linear prediction of random processes spanning a Banach space. In particular, the weak parallelogram laws furnish coefficient growth estimates, Baxter-type inequalities, and criteria for regularity.
Chebyshev Polynomials And The Frohman-Gelca Formula, Heather M. Russell, Hoel Queffelec
Chebyshev Polynomials And The Frohman-Gelca Formula, Heather M. Russell, Hoel Queffelec
Department of Math & Statistics Faculty Publications
Using Chebyshev polynomials, C. Frohman and R. Gelca introduced a basis of the Kauffman bracket skein module of the torus. This basis is especially useful because the Jones–Kauffman product can be described via a very simple Product-to-Sum formula. Presented in this work is a diagrammatic proof of this formula, which emphasizes and demystifies the role played by Chebyshev polynomials.
The Robinson-Schensted Correspondence And A2-Web Bases, Heather M. Russell, Matthew Housley, Julianna Tymoczko
The Robinson-Schensted Correspondence And A2-Web Bases, Heather M. Russell, Matthew Housley, Julianna Tymoczko
Department of Math & Statistics Faculty Publications
We study natural bases for two constructions of the irreducible representation of the symmetric group corresponding to [n; n; n]: the reduced web basis associated to Kuperberg's combinatorial description of the spider category; and the left cell basis for the left cell construction of Kazhdan and Lusztig. In the case of [n; n], the spider category is the Temperley-Lieb category; reduced webs correspond to planar matchings, which are equivalent to left cell bases. This paper compares the image of these bases under classical maps: the Robinson-Schensted algorithm between permutations and Young tableaux and Khovanov-Kuperberg's bijection between …
A Survey On Reverse Carleson Measures, Emmanuel Fricain, Andreas Hartmann, William T. Ross
A Survey On Reverse Carleson Measures, Emmanuel Fricain, Andreas Hartmann, William T. Ross
Department of Math & Statistics Faculty Publications
This is a survey on reverse Carleson measures for various Hilbert spaces of analytic functions. These spaces include the Hardy, Bergman, certain harmonically weighted Dirichlet, Paley-Wiener, Fock, model (backward shift invariant), and de Branges-Rovnyak spaces. The reverse Carleson measure for backward shift invariant subspaces in the non-Hilbert situation is new.
Weak Parallelogram Laws On Banach Spaces And Applications To Prediction, R. Cheng, William T. Ross
Weak Parallelogram Laws On Banach Spaces And Applications To Prediction, R. Cheng, William T. Ross
Department of Math & Statistics Faculty Publications
This paper concerns a family of weak parallelogram laws for Banach spaces. It is shown that the familiar Lebesgue spaces satisfy a range of these inequalities. Connections are made to basic geometric ideas, such as smoothness, convexity, and Pythagorean-type theorems. The results are applied to the linear prediction of random processes spanning a Banach space. In particular, the weak parallelogram laws furnish coefficient growth estimates, Baxter-type inequalities, and criteria for regularity.