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 |
Download $q$-Difference Operators, Orthogonal Polynomials, and Symmetric Expansions Book in PDF, Epub and Kindle
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 | : M Zuhair Nashed |
Publisher | : World Scientific |
Total Pages | : 577 |
Release | : 2018-01-12 |
Genre | : Mathematics |
ISBN | : 981322889X |
Download Frontiers In Orthogonal Polynomials And Q-series Book in PDF, Epub and Kindle
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 | : Marc Aristide Rieffel |
Publisher | : American Mathematical Soc. |
Total Pages | : 106 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 0821835181 |
Download Gromov-Hausdorff Distance for Quantum Metric Spaces/Matrix Algebras Converge to the Sphere for Quantum Gromov-Hausdorff Distance Book in PDF, Epub and Kindle
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 |
Download $S$-Modules in the Category of Schemes Book in PDF, Epub and Kindle
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 |
Download On the Classification of Polish Metric Spaces Up to Isometry Book in PDF, Epub and Kindle
Author | : Reinhard Höpfner |
Publisher | : American Mathematical Soc. |
Total Pages | : 105 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 082183231X |
Download Limit Theorems for Null Recurrent Markov Processes Book in PDF, Epub and Kindle
Author | : Masaaki Furusawa |
Publisher | : American Mathematical Soc. |
Total Pages | : 158 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821833286 |
Download On Central Critical Values of the Degree Four $L$-functions for $\mathrm {GSp}(4)$: The Fundamental Lemma Book in PDF, Epub and Kindle
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}].
Author | : Alan Forrest |
Publisher | : American Mathematical Soc. |
Total Pages | : 137 |
Release | : 2002 |
Genre | : Mathematics |
ISBN | : 0821829653 |
Download Topological Invariants for Projection Method Patterns Book in PDF, Epub and Kindle
This memoir develops, discusses and compares a range of commutative and non-commutative invariants defined for projection method tilings and point patterns. The projection method refers to patterns, particularly the quasiperiodic patterns, constructed by the projection of a strip of a high dimensional integer lattice to a smaller dimensional Euclidean space. In the first half of the memoir the acceptance domain is very general - any compact set which is the closure of its interior - while in the second half the authors concentrate on the so-called canonical patterns. The topological invariants used are various forms of $K$-theory and cohomology applied to a variety of both $C DEGREES*$-algebras and dynamical systems derived from such a p
Author | : Helge Glöckner |
Publisher | : American Mathematical Soc. |
Total Pages | : 150 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821832565 |
Download Positive Definite Functions on Infinite-Dimensional Convex Cones Book in PDF, Epub and Kindle
A memoir that studies positive definite functions on convex subsets of finite- or infinite-dimensional vector spaces. It studies representations of convex cones by positive operators on Hilbert spaces. It also studies the interplay between positive definite functions and representations of convex cones.
Author | : Stefano Marmi |
Publisher | : American Mathematical Soc. |
Total Pages | : 98 |
Release | : 2003 |
Genre | : Mathematics |
ISBN | : 0821833251 |
Download Quasianalytic Monogenic Solutions of a Cohomological Equation Book in PDF, Epub and Kindle
We prove that the solutions of a cohomological equation of complex dimension one and in the analytic category have a monogenic dependence on the parameter. This cohomological equation is the standard linearized conjugacy equation for germs of holomorphic maps in a neighborhood of a fixed point.