In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. There are three main claims concerning these spaces that are covered: determining the integrability classes of the trace of Riesz potentials of an arbitrary Morrey function; determining the dimensions of singular sets of weak solutions of PDE (e.g. The Meyers-Elcart System); and determining whether there are any "full" interpolation results for linear operators between Morrey spaces.
This book will serve as a useful reference to graduate...
In this set of lecture notes, the author includes some of the latest research on the theory of Morrey Spaces associated with Harmonic Analysis. The...
These include fractal spaces, wavelets with composite dilations, and abstract constructions of GMRAs beyond the usual setting of L^2(R^n). This account of recent developments in wavelet theory will appeal to researchers and graduate students with an interest in multiscale analysis from a pure or applied perspective.
These include fractal spaces, wavelets with composite dilations, and abstract constructions of GMRAs beyond the usual setting of L^2(R^n). This acco...
Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important mathematical advances
Presents new results and applications to diverse fields such as geometry, number theory, and analysis
Contributors are leading experts in their respective fields
Will be of interest to both pure and applied mathematicians
Explores relationship between Fourier Analysis, convex geometry, and related areas; in the past, study of this relationship has led to important ma...
"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...
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...
Recently there has been intense research activity on the subject of wavelet/subband theory and application. Experts in such diverse fields as mathematics, physics, electrical engineering and image processing have provided original and pioneering works and results. But this diversity, while rich and productive, has lead to a sense of fragmentation, especially to those new to the field, and nonspecialists, trying to understand the connections between the different aspects of wavelet and subband theory.
The book is designed to present an understanding of wavelets and their development...
Recently there has been intense research activity on the subject of wavelet/subband theory and application. Experts in such diverse fields as mathe...
Provides a digest of the current developments, open questions and unsolved problems likely to determine a new frontier for future advanced study and research in the rapidly growing areas of wavelets, wavelet transforms, signal analysis, and signal and image processing. Ideal reference work for advanced students and practitioners in wavelets, and wavelet transforms, signal processing and time-frequency signal analysis. Professionals working in electrical and computer engineering, applied mathematics, computer science, biomedical engineering, physics, optics, and fluid mechanics will also...
Provides a digest of the current developments, open questions and unsolved problems likely to determine a new frontier for future advanced study an...
. . . that is what learning is. You suddenly understand something you've un- derstood all your life, but in a new way. Various transforms have been widely used in diverse applications of science, engineering and technology. New transforms are emerging to solve many problems, which may have been left unsolved in the past, or newly created by modern science or technologies. Various meth- ods have been continuously reported to improve the implementation of these transforms. Early developments of fast algorithms for discrete transforms have significantly stimulated the advance of digital signal...
. . . that is what learning is. You suddenly understand something you've un- derstood all your life, but in a new way. Various transforms have been wi...
This textbook presents the mathematics that is foundational to multimedia applications. Featuring a rigorous survey of selected results from algebra and analysis, the work examines tools used to create application software for multimedia signal processing and communication.
Replete with exercises, sample programs in Standard C, and numerous illustrations, Mathematics for Multimedia is an ideal textbook for upper undergraduate and beginning graduate students in computer science and mathematics who seek an innovative approach to contemporary mathematics with...
This textbook presents the mathematics that is foundational to multimedia applications. Featuring a rigorous survey of selected results from algebr...
Harmonic analysis is a venerable part of modern mathematics. Its roots began, perhaps, with late eighteenth-century discussions of the wave equation. Using the method of separation of variables, it was realized that the equation could be solved with a data function of the form?(x)= sin jx for j? Z.Itwasnaturaltoask, using the philosophy of superposition, whether the equation could then be solved with data on the interval 0, ?] consisting of a nite linear combinationof the sin jx. With an af rmative answer to that question, one is led to ask about in?nite linear combinations. This was an...
Harmonic analysis is a venerable part of modern mathematics. Its roots began, perhaps, with late eighteenth-century discussions of the wave equation. ...
