Deep connections exist between harmonic and appliedanalysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and fea...
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ISBN:
(数字)9783030866648
ISBN:
(纸本)9783030866631;9783030866662
Deep connections exist between harmonic and appliedanalysis and the diverse yet connected topics of machine learning, data analysis, and imaging science. This volume explores these rapidly growing areas and features contributions presented at the second and third editions of the Summer Schools on appliedharmonicanalysis, held at the University of Genova in 2017 and 2019. Each chapter offers an introduction to essential material and then demonstrates connections to more advanced research, with the aim of providing an accessible entrance for students and researchers. Topics covered include ill-posed problems; concentration inequalities; regularization and large-scale machine learning; unitarization of the radon transform on symmetric spaces; and proximal gradient methods for machine learning and imaging.
Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwave...
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ISBN:
(数字)9783319685304
ISBN:
(纸本)9783319685298;9783319886176
Further, as an advanced reference guide for experienced researchers and practitioners in mathematics, physics, and engineering, the book addresses in detail a wide range of basic and advanced topics (such as multiwavelets/multiframelets in Sobolev spaces and directional framelets) in wavelet theory, together with systematic mathematical analysis, concrete algorithms, and recent developments in and applications of framelets and wavelets.
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for sol...
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ISBN:
(数字)9783319925868
ISBN:
(纸本)9783319925844;9783030064679
Continuing the authors’ multivolume project, this text considers the theory of distributions from an applied perspective, demonstrating how effective a combination of analytic and probabilistic methods can be for solving problems in the physical and engineering sciences.;covered foundational topics such as distributional and fractional calculus, the integral transform, and wavelets, and;explored linear and nonlinear dynamics in continuous media. With this volume, the scope is extended to the use of distributional tools in the theory of generalized stochastic processes and fields, and in anomalous fractional random dynamics.;Chapters cover topics such as probability distributions; generalized stochastic processes, Brownian motion, and the white noise; stochastic differential equations and generalized random fields; Burgers turbulence and passive tracer transport in Burgers flows; and linear, nonlinear, and multiscale anomalous fractional dynamics in continuous media. The needs of the applied-sciences audience are addressed by a careful and rich selection of examples arising in real-life industrial and scientific labs and a thorough discussion of their physical significance. Numerous illustrations generate a better understanding of the core concepts discussed in the text, and a large number of exercises at the end of each chapter expand on these concepts.;is intended to fill a gap in the typical undergraduate engineering/physical sciences curricula, and as such it will be a valuable resource for researchers and graduate students working in these areas. The only prerequisites are a three-four semester calculus sequence (including ordinary differential equations, Fourier series, complex variables, and linear algebra), and some probability theory, but basic definitions and facts are covered as needed. An appendix also provides background material concerning the Dirac-delta and other distributions.
Methods of signal analysis represent a broad research topic with applications in many disciplines, including engineering, technology, biomedicine, seismography, eco nometrics, and many others based upon the proc...
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ISBN:
(数字)9781461217688
ISBN:
(纸本)9780817640422;9781461272731
Methods of signal analysis represent a broad research topic with applications in many disciplines, including engineering, technology, biomedicine, seismography, eco nometrics, and many others based upon the processing of observed variables. Even though these applications are widely different, the mathematical background be hind them is similar and includes the use of the discrete Fourier transform and z-transform for signal analysis, and both linear and non-linear methods for signal identification, modelling, prediction, segmentation, and classification. These meth ods are in many cases closely related to optimization problems, statistical methods, and artificial neural networks. This book incorporates a collection of research papers based upon selected contri butions presented at the First European Conference on Signal analysis and Predic tion (ECSAP-97) in Prague, Czech Republic, held June 24-27, 1997 at the Strahov Monastery. Even though the Conference was intended as a European Conference, at first initiated by the European Association for Signal Processing (EURASIP), it was very gratifying that it also drew significant support from other important scientific societies, including the lEE, Signal Processing Society of IEEE, and the Acoustical Society of America. The organizing committee was pleased that the re sponse from the academic community to participate at this Conference was very large; 128 summaries written by 242 authors from 36 countries were received. In addition, the Conference qualified under the Continuing Professional Development Scheme to provide PD units for participants and contributors.
This volume is dedicated to John Benedetto. It seems just yesterday that we celebrated his 60th birthday in a memorable conference in College Park. Yet that was October of 1999, and already more than six years have pa...
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ISBN:
(数字)9780817645045
ISBN:
(纸本)9780817637781
This volume is dedicated to John Benedetto. It seems just yesterday that we celebrated his 60th birthday in a memorable conference in College Park. Yet that was October of 1999, and already more than six years have passed. But John is still too young to be fully honored by a single foreword,or even a singlevolume,thatattemptstosummarizetheimpactofhisworkonharmonicanalysis, his students, and his *** his continuing high (and even increasing) level of activities, his list of “lifetime achievements” is surely far from complete. Even so, we will make an attempt in this foreword to take a look back, to see the major lines of his work and activities during the past 40 years of his life as a scientist, and to learn from his biography (and bibliography) how the ?eld of harmonicanalysis has changed over the years, and in particular to see the vibrant role that John has taken in this process. John’s ?rst paper appeared in 1965, when he was 25 years old, and his ?rst book (the Springer Lecture Notes on harmonicanalysis on Totally D- connected Sets) when he was 31. By that time he had already published on the subjects of Tauberian algebras, in the theory of generalized functions, and on questions related to spectral synthesis. His work on this latter topic continued through the 1970s, culminating in the insightful volume Spectral Synthesis (1975). Only a year later, his text Real Variables and Integration with Historical Notes appeared.
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