Q Difference Operators Orthogonal Polynomials And Symmetric Expansions
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Author | : Douglas Bowman |
Publisher | : American Mathematical Soc. |
Total Pages | : 73 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 082182774X |
The author explores ramifications and extensions of a $q$-difference operator method first used by L.J. Rogers for deriving relationships between special functions involving certain fundamental $q$-symmetric polynomials. In special cases these symmetric polynomials reduce to well-known classes of orthogonal polynomials. A number of basic properties of these polynomials follow from this approach. This leads naturally to the evaluation of the Askey-Wilson integral and generalizations. Expansions of certain generalized basic hypergeometric functions in terms of the symmetric polynomials are also found. This provides a quick route to understanding the group structure generated by iterating the two-term transformations of these functions. Some infrastructure is also laid for more general investigations in the future
Author | : Masatoshi Noumi |
Publisher | : Springer Nature |
Total Pages | : 137 |
Release | : |
Genre | : |
ISBN | : 9819945879 |
Author | : M Zuhair Nashed |
Publisher | : World Scientific |
Total Pages | : 577 |
Release | : 2018-01-12 |
Genre | : Mathematics |
ISBN | : 981322889X |
This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.
Author | : Robert Bieri |
Publisher | : American Mathematical Soc. |
Total Pages | : 105 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821831844 |
Generalizing the Bieri-Neumann-Strebel-Renz Invariants, this Memoir presents the foundations of a theory of (not necessarily discrete) actions $\rho$ of a (suitable) group $G$ by isometries on a proper CAT(0) space $M$. The passage from groups $G$ to group actions $\rho$ implies the introduction of 'Sigma invariants' $\Sigmak(\rho)$ to replace the previous $\Sigmak(G)$ introduced by those authors. Their theory is now seen as a special case of what is studied here so that readers seeking a detailed treatment of their theory will find it included here as a special case. We define and study 'controlled $k$-connectedness $(CCk)$' of $\rho$, both over $M$ and over end points $e$ in the 'boundary at infinity' $\partial M$; $\Sigmak(\rho)$ is by definition the set of all $e$ over which the action is $(k-1)$-connected. A central theorem, the Boundary Criterion, says that $\Sigmak(\rho) = \partial M$ if and only if $\rho$ is $CC{k-1}$ over $M$.An Openness Theorem says that $CCk$ over $M$ is an open condition on the space of isometric actions $\rho$ of $G$ on $M$. Another Openness Theorem says that $\Sigmak(\rho)$ is an open subset of $\partial M$ with respect to the Tits metric topology. When $\rho(G)$ is a discrete group of isometries the property $CC{k-1}$ is equivalent to ker$(\rho)$ having the topological finiteness property type '$F_k$'. More generally, if the orbits of the action are discrete, $CC{k-1}$ is equivalent to the point-stabilizers having type $F_k$. In particular, for $k=2$ we are characterizing finite presentability of kernels and stabilizers. Examples discussed include: locally rigid actions, translation actions on vector spaces (especially those by metabelian groups
Author | : Jindřich Zapletal |
Publisher | : American Mathematical Soc. |
Total Pages | : 158 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821834509 |
Focuses on the relationship between definable forcing and descriptive set theory; the forcing serves as a tool for proving independence of inequalities between cardinal invariants of the continuum.
Author | : Marc Aristide Rieffel |
Publisher | : American Mathematical Soc. |
Total Pages | : 106 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821835181 |
By a quantum metric space we mean a $C DEGREES*$-algebra (or more generally an order-unit space) equipped with a generalization of the usual Lipschitz seminorm on functions which one associates to an ordinary metric. We develop for compact quantum metric spaces a version of Gromov-Hausdorff di
Author | : Po Hu |
Publisher | : American Mathematical Soc. |
Total Pages | : 141 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821829564 |
Gives a theory $S$-modules for Morel and Voevodsky's category of algebraic spectra over an arbitrary field $k$. This work also defines universe change functors, as well as other important constructions analogous to those in topology, such as the twisted half-smash product.
Author | : Su Gao |
Publisher | : American Mathematical Soc. |
Total Pages | : 93 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821831909 |
Author | : Reinhard Höpfner |
Publisher | : American Mathematical Soc. |
Total Pages | : 105 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082183231X |
Author | : Masaaki Furusawa |
Publisher | : American Mathematical Soc. |
Total Pages | : 158 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821833286 |
Proves two equalities of local Kloosterman integrals on $\mathrm{GSp}\left(4\right)$, the group of $4$ by $4$ symplectic similitude matrices. This book conjectures that both of Jacquet's relative trace formulas for the central critical values of the $L$-functions for $\mathrm{g1}\left(2\right)$ in [{J1}] and [{J2}].