Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved problems that still exist in coding theory. A well-established, yet still highly relevant branch of mathematics, the theory of error-correcting codes is concerned with reliably transmitting data over a 'noisy' channel. Despite its frequent use in a range of contexts--the first close-up pictures of the surface of Mars, taken by the NASA spacecraft Mariner 9, were transmitted back to Earth using a Reed-Muller code--the subject still contains interesting...
Using an original mode of presentation, and emphasizing the computational nature of the subject, this book explores a number of the unsolved proble...
Increasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband signals. This concise but comprehensive monograph is the first to be devoted specifically to this subdiscipline, providing a thorough investigation of its theory and applications. Through cutting-edge numerical methods, it develops the tools for applications not only to communications engineering, but also to optical engineering, geosciences, planetary sciences, and biomedicine.
With broad coverage and a careful balance between rigor and...
Increasingly important in the field of communications, the study of time and band limiting is crucial for the modeling and analysis of multiband si...
Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means of encoding isotropic phenomena. Directional multiscale systems, particularly shearlets, are now having the same dramatic impact on the encoding of multidimensional signals. Since its introduction about five years ago, the theory of shearlets has rapidly developed and gained wide recognition as the superior way of achieving a truly unified treatment in both a continuous and a digital setting. By now, it has reached maturity as a research field, with...
Over the last 20 years, multiscale methods and wavelets have revolutionized the field of applied mathematics by providing an efficient means of enc...
Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, and erasures, as well as their ability to capture valuable signal characteristics. More recently, finite frame theory has grown into an important research topic in its own right, with a myriad of applications to pure and applied mathematics, engineering, computer science, and other areas. The number of research publications, conferences, and workshops on this topic has increased dramatically over the past few years, but no survey paper or...
Hilbert space frames have long served as a valuable tool for signal and image processing due to their resilience to additive noise, quantization, a...
During the last few decades, the subject of potential theory has not been overly popular in the mathematics community. Neglected in favor of more abstract theories, it has been taught primarily where instructors have ac- tively engaged in research in this field. This situation has resulted in a scarcity of English language books of standard shape, size, and quality covering potential theory. The current book attempts to fill that gap in the literature. Since the rapid development of high-speed computers, the remarkable progress in highly advanced electronic measurement concepts, and, most of...
During the last few decades, the subject of potential theory has not been overly popular in the mathematics community. Neglected in favor of more abst...
The 7th International Workshop in Analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi- mately 60 mathematicians. The principal theme of the workshop shares the title of this volume and the latter is a direct outgrowth of the workshop. IWAA was founded in 1984 by Professor Caslav V. Stanojevic. The first meeting was held in the resort complex Kupuri, Yugoslavia, June 1-10, 1986, with two pilot meetings preceding. The Organization Committee to- gether with the Advisory Committee (R. P. Boas, R. R. Goldberg, J. P. Kahne) set forward the...
The 7th International Workshop in Analysis and its Applications (IWAA) was held at the University of Maine, June 1-6, 1997 and featured approxi- matel...
"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta del Sol, VII, 4, 1996. A Personal Prehistory In 1972 I started cooperating with members of the Biodynamics Research Unit at the Mayo Clinic in Rochester, Minnesota, which was under the direction of Earl H. Wood. At that time, their ambitious (and eventually realized) dream was to build the Dynamic Spatial Reconstructor (DSR), a device capable of collecting data regarding the attenuation of X-rays through the human body fast enough for...
"La narraci6n literaria es la evocaci6n de las nostalgias. " ("Literary narration is the evocation of nostalgia. ") G. G. Marquez, interview in Puerta...
Overview For over a decade now, wavelets have been and continue to be an evolving subject of intense interest. Their allure in signal processing is due to many factors, not the least of which is that they offer an intuitively satisfying view of signals as being composed of little pieces of wa'ues. Making this concept mathematically precise has resulted in a deep and sophisticated wavelet theory that has seemingly limitless applications. This book and its supplementary hands-on electronic: component are meant to appeal to both students and professionals. Mathematics and en- gineering students...
Overview For over a decade now, wavelets have been and continue to be an evolving subject of intense interest. Their allure in signal processing is du...
The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre- dominates as questions of convergence are not considered. Our approach emphasizes the unifying role played by group structures on the development of theory and algorithms. This book consists of two main parts. The first treats Weyl-Heisenberg representations over finite abelian groups and the second deals with mul- tirate filter structures over free abelian groups of finite rank. In both, the methods are dimensionless and coordinate-free and apply...
The aim of this work is to present several topics in time-frequency analysis as subjects in abelian group theory. The algebraic point of view pre- dom...
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems which is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important to practioners and researchers. The goal of the book is to give the reader, specialist and non-specialist useable and modern mathematical tools in their research and analysis. This new text is intended for graduate students and researchers in applied mathematics, physical sciences and engineering. The...
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and e...
