National Symposium on Functional Analysis, Optimization and Applications

The University of Newcastle
9-19 March, Workshop
20-21 March, Miniconference

Volume 36 in the Proceedings of the Centre for Mathematics and its Applications

Preface

This volume contains papers by participants in the National Symposium on Functional Analysis, Optimization and Applications held at the University of Newcastle in March 1998. The Symposium was a joint acivity organised by the Department of Mathematics and the Centre for Integrated dynamics and Control (CIDAC), which is associated with the Department of Electrical and Computer Engineering, all at the University of Newcastle. Our special guest leading the symposium was Professor Jonathan Borwein from Simon Fraser University, British Columbia, Canada, whose visit was sponsored by CIDAC. From Monday 9th until Thursday 19th March we met in workshop sessions where two papers were read each morning (with discussion afterwards) and on Friday 20th and Saturday 21st March, we held a formal miniconference session where seven papers were presented each day.

We had participants from the Universities of Western Australia, Murdoch, Melbourne, Ballarat, Sydney, NSW, the Australian Catholic, and Newcastle. We also included visitors from the Universities of Toronto and Simon Fraser (Canada), Seville (Spain) and Harbin (China).

The aim of the symposium was to achieve some cross fertilisation of ideas between mathematicians working in functional analysis and engineers whose main concern is optimal control and estimation. In our opinion, much useful dialogue between workers in these fields was exchanged.

This volume contains the refereed papers of some of the participants. Although the papers themselves are generally identifiable as being from one of the two participating groups of mathematicians or engineers it is hoped that the publication of the papers in one volume will help promote more of the inter-field discussion that we enjoyed in our symposium.

We wish to thank the Centre for Mathematics and its Applications for including us in their National Symposium Program, supporting our Australian participants, and for publishing these proceedings. We are grateful for the secretarial support given by Mrs Jan Garnsey from the Department of Mathematics at the University of Newcastle, and Mrs Annette Hughes, Administrative Officer to CMA.

Of course we also thank all our colleagues who participated in the dialogue and contributed talks and papers to promote it.

John Giles, Brett Ninness
(Organisers and editors)

Contents

Conical open mapping theorems and regularity Heinz H. Bauschke and Jonathan M. Borwein	1
An algebraic approach to optimal output decoupling by output feedback control Thomas S. Brinsmead and Graham C. Goodwin	11
Non-differentiable invex B.D.Craven	25
Strict property (M) in Banach spaces Yunan Cui	29
Properties of finite rank operators that arise in approximation of integral operators related to linear dynamical systems José A. De Doná, Graham C. Goodwin and Richard H. Middleton	39
Exposing conditions implying uniformity of rotundity John R. Giles and Warren B. Moors	49
Worst-case identification of linear systems: existence and complexity D.W. Hadwin, K.J. Harrison and J.A. Ward	53
Design of multi-channel linear phase FIR filters Gustav Ljungars and Minyue Fu	67
Generalised Fourier and Toeplitz results for rational orthonormal bases Brett Ninness, Håkan Hjalmarsson and Fredrik Gustafsson	87
Voltage graphs David Pask and Trent Yeend	99
Dynamical systems and operator algebras Iain Raeburn	109
Groups, representations and Haagerup's inequality for buildings Jacqui Ramagge	121
Operator theoretic problems for Fourier multipliers in Lp(R) W.J. Ricker	127
Some properties of increasing convex-along-rays functions A.M. Rubinov	153
On a calculus of discontinuous functions used in interfacial flow modeling Scott Sciffer	169
Maps which have fixed points for any Banach space Brailey Sims	179
Limitations on achievable tracking accuracy for single-input two-output systems Andrew Woodyatt	185