Miniconference on Operators in Analysis

Macquarie University, Sydney, NSW, September 25-27, 1989

Volume 24 in the Proceedings of the Centre for Mathematical Analysis

Preface

This volume contains the proceedings of a three day miniconference on operator theory, partial differential equations, and related areas of analysis, held at Macquarie University, Sydney, in September 1989, under the sponsorship of the Centre for Mathematical Analysis (Australian National University) whose financial assistance is gratefully acknowledged.

We wish to express our appreciation to all the participants, to those who contributed to this volume, to those who so willingly assisted us with the organization, and to those who typed the manuscripts for this volume. We especially thank Marilyn Gray and Dorothy Nash whose superb organizational skills helped to make this conference a success.

Ian Doust, Brian Jefferies, Chun Li and Alan M^cIntosh
(Editors)

Contents

Preface	(i)
Schauder estimates on Lie groups Robert J. Burns and Derek W. Robinson	1
A note on martingales with respect to complex measures M.G. Cowling, G.I. Gaudry and T. Qian	10
Surface measures - maximal functions and Fourier transforms Michael Cowling and Giancarlo Mauceri	28
Measures of semi-noncompactness and AM-mappings Sun Daqing	38
A general Markus inequality Peter G. Dodds, Theresa K.-Y. Dodds and Ben de Pagter	47
Remarks on non-commutative interpolation Peter G. Dodds, Theresa K.-Y. Dodds and Ben de Pagter	58
Solvability of differential operators on semiradial semidirect products A.H. Dooley	79
An example in the theory of spectral and well-bounded operators Ian Doust	83
H∞ functional calculus of second order elliptic partial differential operators on LP spaces Xuan Thinh Duong	91
An extension of a theorem of Halmos to Orlicz spaces, and an application to Nemitsky operators Grahame Hardy	103
Mixed volumes and connected variational problems N.M. Ivochkina	109
Toeplitz operators on Fock spaces Jan Janas	115
The uniqueness of diffusion semigroups Brian Jefferies	126
Four remarks concerning the Feynman integral Igor Kluvánek	135
The natural generalization of the natural conditions of Ladyzhenskaya and Ural'tseva Gary M. Lieberman	151
Operators of type ω without a bounded H∞ functional calculus Alan McIntosh and Atsushi Yagi	159
Monotone operators and obstacle problems J.H. Michael	173
An invitation to the anti-periodic problem Hiroko Okochi	179
Functional calculus for non-commuting operators A.J. Pryde	197
Boolean algebras of projections of uniform multiplicity one Werner J. Ricker	206
Inner product algebras and the function theory of associated Dirac operators John Ryan	213
Regularity and non-regularity for solutions of prescribed curvature equations John I.E. Urbas	227