Classical Analysis in honour of David Borwein's 80th Birthday / Analyse classique en l'honneur du 80eme anniversaire de David Borwein
(Org: Jonathan Borwein, Dalhousie University, and/et Mike Overton, New York University)
- HEINZ BAUSCHKE, University of Guelph
Asymptotic behaviour of the composition of two resolvents
Consider the problem of finding a point in the intersection of two
nonempty closed convex sets in a Hilbert space. The method of
alternating projections is an iterative attempt to solve this
problem. If the intersection of the two sets is nonempty, then-this
is a classical result due to Bregman-the sequence generated
converges weakly to a common point; otherwise, the sequence either
tends to infinity in norm or it possesses two cluster points realizing
the gap between the two sets.
In this talk, I will discuss recent extensions of this result
concerning the asymptotic behaviour of resolvents and Bregman proximal
Based on joint work with Patrick Combettes (Paris 6), Dominikus Noll
(Toulouse), and Simeon Reich (Technion).
- GRAHAME BENNETT, Indiana University, Bloomington, IN 47405, USA
Summability for those without
We consider several attractive and easy-to-state problems. These have
no apparent connection with Summability Theory, yet their solutions
are all centered upon one of David Borwein's favorite topics:
- PETER BORWEIN, Mathematics Department, Simon Fraser University
The Mahler Measure of Polynomials with Odd Coefficients
We resolve an old conjecture of Schinzel and Zassenhaus for the class
of polynomials with no cyclotomic factors whose coefficients are all
More generally, we solve the problems of Lehmer for irreducible
polynomials in the above class by showing that the Mahler measure (the
L0 norm) of such polynomials is bounded away from 1.
- PETER CASS, University of Western Ontario, London, Ontario
A Retrospective on David Borwein's contribution to
A retrospective on David Borwein's contribution to mathematical research.
- MICHAEL OVERTON, Courant Institute of Mathematical Sciences, New York University,
251 Mercer St., New York, NY 10012, USA
Optimal Stability and Eigenvalue Multiplicity
We consider the problem of minimizing over an affine set of square
matrices the maximum of the real parts of the eigenvalues. Such
problems are prototypical in robust control and stability
analysis. Under nondegeneracy conditions, we show that the
multiplicities of the active eigenvalues at a critical matrix remain
unchanged under small perturbations of the problem. Furthermore, each
distinct active eigenvalue corresponds to a single Jordan block. This
behavior is crucial for optimality conditions and numerical
methods. Our techniques blend nonsmooth optimization and matrix
This is joint work with James V. Burke (U. Wash.) and Adrian S. Lewis
- BRUCE SHAWYER, Memorial University of Newfoundland
Tribute and a Plethora of Remarkable Concurrences
This talk is in two parts:
- An appreciation of David Borwein as a colleague, problem solver,
supervisor and person.
- A Plethora of Remarkable Concurrences, dedicated to David
Borwein on his 80th birthday.
There are several examples of concurrence in classical triangle
geometry. For example, the medians, the altitudes, the angle bisectors
and the perpendicular bisectors of the sides.
Here we show that there are a plethora of concurrences with some
- BRUCE WATSON, Memorial University, St. John's, NL
Discrete Power Series Methods
In 1989 and 1990 papers, Maddox and Armitage discretized the
well-known Cesàro and Abel methods. The author extends the
definitions to discrete power series and weighted mean methods and
gives some abelian and tauberian results.
- JIM ZHU, Western Michigan University
A variational proof of Birkhoff's theorem on doubly
In this talk I will give a short and self-contained variational proof
of Birkhoff's theorem asserting that the extreme points of the convex
set of doubly stochastic matrices are the permutation matrices.