With this text, Jonathan Partington explores the application of mathematical analysis to problems of interpolation and engineering, including systems identification, and signal processing and sampling.

This book is devoted to some topical problems and applications of operator theory and its interplay with modern complex analysis. It consists of 20 selected survey papers that represent updated (mainly plenary) addresses to the IWOTA 2000 conference held at Bordeaux from June 13 to 16, 2000. The main subjects of the volume include: - spectral analysis of periodic differential operators and delay equations, stabilizing controllers, Fourier multipliers; - multivariable operator theory, model theory, commutant lifting theorems, coisometric realizations; - Hankel operators and forms; - operator algebras; - the Bellman function approach in singular integrals and harmonic analysis, singular integral operators and integral representations; - approximation in holomorphic spaces. These subjects are unified by the common "operator theoretic approach" and the systematic use of modern function theory techniques.

This volume consists of chapters written by eminent scientists and engineers from the international community and present significant advances in several theories, methods and applications of an interdisciplinary research. These contributions focus on both old and recent developments of Global Optimization Theory, Convex Analysis, Calculus of Variations, Discrete Mathematics and Geometry, as well as several applications to a large variety of concrete problems, including applications of computers to the study of smoothness and analyticity of functions, applications to epidemiological diffusion, networks, mathematical models of elastic and piezoelectric fields, optimal algorithms, stability of neutral type vector functional differential equations, sampling and rational interpolation for non-band-limited signals, recurrent neural network for convex optimization problems and experimental design. The book also contains some review works, which could prove particularly useful for a broader audience of readers in Mathematical and Engineering subjects and especially to graduate students who search for the latest information.

Our understanding of nature is often through nonuniform observations in space or time. In space, one normally observes the important features of an object, such as edges. The less important features are interpolated. History is a collection of important events that are nonuniformly spaced in time. Historians infer between events (interpolation) and politicians and stock market analysts forecast the future from past and present events (extrapolation). The 20 chapters of Nonuniform Sampling: Theory and Practice contain contributions by leading researchers in nonuniform and Shannon sampling, zero crossing, and interpolation theory. Its practical applications include NMR, seismology, speech and image coding, modulation and coding, optimal content, array processing, and digital filter design. It has a tutorial outlook for practising engineers and advanced students in science, engineering, and mathematics. It is also a useful reference for scientists and engineers working in the areas of medical imaging, geophysics, astronomy, biomedical engineering, computer graphics, digital filter design, speech and video processing, and phased array radar.

Advances in Imaging and Electron Physics merges two long-running serials--Advances in Electronics and Electron Physics and Advances in Optical and Electron Microscopy. The series features extended articles on the physics of electron devices (especially semiconductor devices), particle optics at high and low energies, microlithography, image science and digital image processing, electromagnetic wave propagation, electron microscopy, and the computing methods used in all these domains.

Advances in solid state detector arrays, flat panel displays and digital image processing have prompted an increasing variety of sampled imaging products and possibilities. These technology developments provide new opportunities and problems for the design engineer and system analyst - this tutorial's intended reader.

This volume is an outgrowth of the workshop "Applications of Advanced Control Theory to Robotics and Automation, "organized in honor of the 70th birthdays of Petar V. Kokotovic and Salvatore (Turi) Nicosia. Both Petar and Turi have carried out distinguished work in the control community and have long been recognized as mentors, as well as experts and pioneers in the field of automatic control, covering many topics in control theory and several different applications. The variety of their research is reflected in this book, which includes contributions ranging from mathematics to laboratory experiments. The scope of the work is very broad, and although each chapter is self-contained, the book has been organized into thematically related chapters, which in some cases, suggest to the reader a convenient reading sequence. The great variety of topics covered and the almost tutorial writing style used by many of the authors will make this book suitable for both experts in the control field and young researchers who seek a more intuitive understanding of these relevant topics in the field.

The book is motivated by the pivotal issue: what is the performance limit of active control and energy harvesting? It aims to develop systematic design methodologies with a “visualization technique” where the performance limit can be readily determined solely based on visual inspections. Modern technological systems have evolved toward high speed, heavy load, lightweight, flexible operation and extreme conditions, as demonstrated in aerospace, marine, transportation and manufacturing industries. The associated vibration and noise issues have become such problematic that they may significantly confine the performance of the systems, to say the discomfort at least. Through the geometric representation of the performance specifications, fundamental issues such as (1) the existence of feasible controllers; (2) the optimality of controllers; (3) the performance limit of controllers; (4) compromisability among the performance specifications; (5) the synthesis of controllers; and (6) the influence of constraints on optimal solutions can all be resolved within the proposed framework. The state of the art is thus refined with a new approach complementary to those optimization-based routines, where extra effort would have to be exercised to disclose the compromisability of performance specifications. The proposed book will result in a new design methodology—performance limit-oriented active control. It was initiated by the author with the project “Active Control for Performance Limit” (ACPL). A series of fundamental results are obtained and will be disseminated in this book. The results are verified through extensive numerical demonstrations and are expected to provide useful guidance for practical engineering in the vibration and noise industry and research.

Hidenori Kimura, renowned system and control theorist, turned 60 years of age in November, 2001. To celebrate this memorable occasion, his friends, collaborators, and former students gathered from all over the world and held a symposium in his honor on November 1 and 2, 2001, at the Sanjo Conference Hall at the University of Tokyo. Reflecting his current research interests, the symposium was entitled "Cybernetics in the 21st Century: Information and Complexity in Control Theory," and it drew nearly 150 attendees. There were twenty-five lectures, on which the present volume is based. Hidenori Kimura was born on November 3, 1941, in Tokyo, just prior to the outbreak of the Second World War. It is not hard to imagine, then, that his early days, like those of so many of his contemporaries, must have been difficult. Fortunately, the war ended in 1945, and his generation found itself thoroughly occupied with the rebuilding effort and with Japan's uphill journey in the last half-century. He entered the University of Tokyo in 1963, received a B. S. in 1965, an M. S. in 1967, and, in 1970, a Ph. D. degree for his dissertation "A Study of Differential Games. " After obtaining his doctorate, he joined the Department of Control En gineering at Osaka University as a research associate, and in 1973 he was promoted to an associate professor.

Almost a century ago, harmonic analysis entered a (still continuing) Golden Age, with the emergence of many great masters throughout Europe. They created a wealth of profound analytic methods, to be successfully exploited and further developed by succeeding generations. This flourishing of harmonic analysis is today as lively as ever, as the papers presented here demonstrate. In addition to its own ongoing internal development and its basic role in other areas of mathematics, physics and chemistry, financial analysis, medicine, and biological signal processing, harmonic analysis has made fundamental contributions to essentially all twentieth century technology-based human endeavours, including telephone, radio, television, radar, sonar, satellite communications, medical imaging, the Internet, and multimedia. This ubiquitous nature of the subject is amply illustrated. The book not only promotes the infusion of new mathematical tools into applied harmonic analysis, but also to fuel the development of applied mathematics by providing opportunities for young engineers, mathematicians and other scientists to learn more about problem areas in today's technology that might benefit from new mathematical insights.