This volume contains the proceedings of the conferences held in the second half of the Special Year in Harmonic Analysis and Operator Algebras at the Centre for Mathematical Analysis in 1987. There were in fact two conferences, the first held in August and the second somewhat smaller gathering in December. There was a wide variety of participants from many different countries and areas of the subject. Papers ranged from classical Fourier analysis in one and several variables through the theory of representations on abstract as well as Lie groups to the K-theory of C*-algebras.
In addition to these intensive sessions there were regular seminars and informal discussions.
The editors would like to thank the Centre for Mathematical Analysis for putting on this Special Year, and in particular the Director, Professor Neil Trudinger, for proposing the idea and for the generous support of the Special Year. Our thanks go also to Dr John Hutchinson and Professor Leon Simon who were Acting Directors for periods of 1987. The organisation of the Year would have been beyond the capabilities of the editors were it not for the assistance of the administrative staff of the Centre. Our warm thanks go in particular to Mrs Marilyn Gray who by her persistent harrying of us to make decisions and by her efficiency in carrying them out made the Special Year possible. She was ably assisted by Mrs Dorothy Nash and Mrs Jillian Smith; our thanks go to them also. Finally we wish to thank all the participants for their patience and presence and contributions to the mathematical life in Canberra, and on behalf of the restaurateurs of Canberra for keeping them in business.