This volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics. Each paper represents a contribution by Prof. McKean, either alone or together with other researchers, that has had a profound influence in the respective area.

This IMA Volume in Mathematics and its Applications RADAR AND SONAR, PART II is based on the proceedings of the second week of the IMA summer program "Radar and Sonar." Week two was devoted to the presentation of problems and solutions of problems in Radar and Sonar. vVe are grat.eful to Alberto Griinbaum, Marvin Bernfeld and Richard Blahut for organizing the program. We also take this opportunity to thank those agencies whose financial support made the summer program possible: the Air Force Office of Scientific Research, the Army Research Office, the National Science Foundation, the National Security Agency and the Office of Naval Research. A vner Friedman Willard Miller, Jr. PREFACE This volume contains a representative discussion of mathematical problems that arise in radar and sonar and is based on the lectures that were given during the second week of the IMA summer program RADAR AND SONAR, June IS-June 29, 1990. (The first week was devoted to three sets of tutorial lectures and the lecture notes from that part of the program appear in an earlier IMA volume.) The second week was run as a workshop of contributed papers without formal review. The speakers were selected to cover a broad range of problems in this area.

The two volumes of Signal Processing are based on lectures delivered during a six week program held at the IMA from June 27 to August 5, 1988. The first two weeks of the program dealt with general areas and methods of Signal Pro cessing. The problem areas included imaging and analysis of recognition, x-ray crystallography, radar and sonar, signal analysis and 1-D signal processing, speech, vision, and VLSI implementation. The methods discussed included harmonic anal ysis and wavelets, operator theory, algorithm complexity, filtering and estimation, and inverse scattering. The topics of weeks three and four were digital filter, VLSI implementation, and integrable circuit modelling. In week five the concentration was on robust and nonlinear control with aerospace applications, and in week six the emphasis was on problems in radar, sonar and medical imaging. Because of the large overlap between the various one-week and two-week seg ments of the program, we found it more convenient to divide the material somewhat differently. Part I deals with general signal process theory and Part II deals with (i) application of signal processing, (ii) control theory related themes. We are grateful to the scientific organizers: Tom Kailath (Chairman), Louis Aus lander, F. Alberto Grunbaum, J. William Helton, Pramod P. Khargonekar and Sanjoy K. Mitter. We are also grateful for the generous support given to the IMA program by the Office of Naval Research, the Air Force Office of Scientific Research, the Army Research Office and the National Security Agency."

This volume presents a selection of papers by Henry P. McKean, which illustrate the various areas in mathematics in which he has made seminal contributions. Topics covered include probability theory, integrable systems, geometry and financial mathematics. Each paper represents a contribution by Prof. McKean, either alone or together with other researchers, that has had a profound influence in the respective area.