Download or read book Thoughts on Harmonic Analysis on the Sphere Spherical Wavelet Frames and Kernels written by Yizhi Sun and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Four Short Courses on Harmonic Analysis written by Brigitte Forster and published by Springer Science & Business Media. This book was released on 2010 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: Written by internationally renowned mathematicians, this state-of-the-art textbook examines four research directions in harmonic analysis and features some of the latest applications in the field. The work is the first one that combines spline theory, wavelets, frames, and time-frequency methods leading up to a construction of wavelets on manifolds other than Rn. Four Short Courses on Harmonic Analysis is intended as a graduate-level textbook for courses or seminars on harmonic analysis and its applications. The work is also an excellent reference or self-study guide for researchers and practitioners with diverse mathematical backgrounds working in different fields such as pure and applied mathematics, image and signal processing engineering, mathematical physics, and communication theory.
Download or read book Frames and Other Bases in Abstract and Function Spaces written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-06-11 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume I is organized around the theme of frames and other bases in abstract and function spaces, covering topics such as: The advanced development of frames, including Sigma-Delta quantization for fusion frames, localization of frames, and frame conditioning, as well as applications to distributed sensor networks, Galerkin-like representation of operators, scaling on graphs, and dynamical sampling. A systematic approach to shearlets with applications to wavefront sets and function spaces. Prolate and generalized prolate functions, spherical Gauss-Laguerre basis functions, and radial basis functions. Kernel methods, wavelets, and frames on compact and non-compact manifolds.
Download or read book The Functional and Harmonic Analysis of Wavelets and Frames written by Lawrence W. Baggett and published by American Mathematical Soc.. This book was released on 1999 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the past decade, wavelets and frames have emerged as increasingly powerful tools of analysis on $n$-dimension Euclidean space. Both wavelets and frames were studied initially by using classical Fourier analysis. However, in recent years more abstract tools have been introduced, for example, from operator theory, abstract harmonic analysis, von Neumann algebras, etc. The editors of this volume organized a Special Session on the functional and harmonic analysis of wavelets at the San Antonio (TX) Joint Mathematics Meetings. The goal of the session was to focus research attention on these newly-introduced tools and to share the organizers' view that this modern application holds the promise of providing some deeper understanding and fascinating new structures in pure functional analysis. This volume presents the fruitful results of the lively discussions that took place at the conference
Download or read book Harmonic Analysis written by María Cristina Pereyra and published by American Mathematical Soc.. This book was released on 2012 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).
Download or read book A Panorama of Harmonic Analysis written by Steven G. Krantz and published by American Mathematical Soc.. This book was released on 2019-07-03 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Panorama of Harmonic Analysis treats the subject of harmonic analysis, from its earliest beginnings to the latest research. Following both an historical and a conceptual genesis, the book discusses Fourier series of one and several variables, the Fourier transform, spherical harmonics, fractional integrals, and singular integrals on Euclidean space. The climax of the book is a consideration of the earlier ideas from the point of view of spaces of homogeneous type. The book culminates with a discussion of wavelets-one of the newest ideas in the subject. A Panorama of Harmonic Analysis is intended for graduate students, advanced undergraduates, mathematicians, and anyone wanting to get a quick overview of the subject of cummutative harmonic analysis. Applications are to mathematical physics, engineering and other parts of hard science. Required background is calculus, set theory, integration theory, and the theory of sequences and series.
Download or read book Recent Applications of Harmonic Analysis to Function Spaces Differential Equations and Data Science written by Isaac Pesenson and published by Birkhäuser. This book was released on 2017-08-09 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second of a two volume set on novel methods in harmonic analysis, this book draws on a number of original research and survey papers from well-known specialists detailing the latest innovations and recently discovered links between various fields. Along with many deep theoretical results, these volumes contain numerous applications to problems in signal processing, medical imaging, geodesy, statistics, and data science. The chapters within cover an impressive range of ideas from both traditional and modern harmonic analysis, such as: the Fourier transform, Shannon sampling, frames, wavelets, functions on Euclidean spaces, analysis on function spaces of Riemannian and sub-Riemannian manifolds, Fourier analysis on manifolds and Lie groups, analysis on combinatorial graphs, sheaves, co-sheaves, and persistent homologies on topological spaces. Volume II is organized around the theme of recent applications of harmonic analysis to function spaces, differential equations, and data science, covering topics such as: The classical Fourier transform, the non-linear Fourier transform (FBI transform), cardinal sampling series and translation invariant linear systems. Recent results concerning harmonic analysis on non-Euclidean spaces such as graphs and partially ordered sets. Applications of harmonic analysis to data science and statistics Boundary-value problems for PDE's including the Runge–Walsh theorem for the oblique derivative problem of physical geodesy.
Download or read book Harmonic Analysis and Approximation on the Unit Sphere written by Kunyang Wang and published by . This book was released on 2000 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Tutorials on Multiresolution in Geometric Modelling written by Armin Iske and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the only textbook available on multiresolution methods in geometric modeling, a central topic in visualization, which is of great importance for industrial applications. Written in tutorial form, the book is introductory in character, and includes supporting exercises. Other supplementary material and software can be downloaded from the website www.ma.tum.de/primus 2001/.
Download or read book Random Fields on the Sphere written by Domenico Marinucci and published by Cambridge University Press. This book was released on 2011-08-25 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors present a comprehensive analysis of isotropic spherical random fields, with a view towards applications in cosmology. Any mathematician or statistician interested in these applications, especially the booming area of cosmic microwave background (CMB) radiation data analysis, will find the mathematical foundation they need in this book.
Download or read book Coherent States Wavelets and Their Generalizations written by Syed Twareque Ali and published by Springer Science & Business Media. This book was released on 2013-10-30 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition is fully updated, covering in particular new types of coherent states (the so-called Gazeau-Klauder coherent states, nonlinear coherent states, squeezed states, as used now routinely in quantum optics) and various generalizations of wavelets (wavelets on manifolds, curvelets, shearlets, etc.). In addition, it contains a new chapter on coherent state quantization and the related probabilistic aspects. As a survey of the theory of coherent states, wavelets, and some of their generalizations, it emphasizes mathematical principles, subsuming the theories of both wavelets and coherent states into a single analytic structure. The approach allows the user to take a classical-like view of quantum states in physics. Starting from the standard theory of coherent states over Lie groups, the authors generalize the formalism by associating coherent states to group representations that are square integrable over a homogeneous space; a further step allows one to dispense with the group context altogether. In this context, wavelets can be generated from coherent states of the affine group of the real line, and higher-dimensional wavelets arise from coherent states of other groups. The unified background makes transparent an entire range of properties of wavelets and coherent states. Many concrete examples, such as coherent states from semisimple Lie groups, Gazeau-Klauder coherent states, coherent states for the relativity groups, and several kinds of wavelets, are discussed in detail. The book concludes with a palette of potential applications, from the quantum physically oriented, like the quantum-classical transition or the construction of adequate states in quantum information, to the most innovative techniques to be used in data processing. Intended as an introduction to current research for graduate students and others entering the field, the mathematical discussion is self-contained. With its extensive references to the research literature, the first edition of the book is already a proven compendium for physicists and mathematicians active in the field, and with full coverage of the latest theory and results the revised second edition is even more valuable.
Download or read book Gravity Geoid and Space Missions written by Christopher Jekeli and published by Springer Science & Business Media. This book was released on 2005-12-28 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: The lAG International Symposium on Gravity, Geoid, and Space Missions 2004 (GGSM2004) was lield in the beautiful city of Porto, Portugal, from 30 August to 3 September 2004. This symposium encompassed the themes of Commission 2 (Gravity Field) of the newly structured lAG, as well as interdisciplinary topics related to geoid and gravity modeling, with special attention given to the current and planned gravi- dedicated satellite missions. The symposium also followed in the tradition of mid-term meetings that were held between the quadrennial joint meetings of the International Geoid and Gravity Commissions. The previous mid-term meetings were the International Symposia on Gravity, Geoid, and Marine Geodesy (Tokyo, 1996), and Gravity, Geoid, and Geodynamics (Banff, 2000). GGSM2004 aimed to bring together scientists from different areas in the geosciences, working with gravity and geoid related problems, both from the theoretical and practical points of view. Topics of interest included the integration of heterogeneous data and contributions from satellite and airborne techniques to the study of the spatial and temporal variations of the gravity field. In addition to the special focus on the CHAMP, GRACE, and GOCE satellite missions, attention was also directed toward projects addressing topographic and ice field mapping using SAR, LIDAR, and laser altimetry, as well as missions and studies related to planetary geodesy.
Download or read book Multiscale Analysis and Nonlinear Dynamics written by Misha Meyer Pesenson and published by John Wiley & Sons. This book was released on 2013-09-13 with total page 307 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since modeling multiscale phenomena in systems biology and neuroscience is a highly interdisciplinary task, the editor of the book invited experts in bio-engineering, chemistry, cardiology, neuroscience, computer science, and applied mathematics, to provide their perspectives. Each chapter is a window into the current state of the art in the areas of research discussed and the book is intended for advanced researchers interested in recent developments in these fields. While multiscale analysis is the major integrating theme of the book, its subtitle does not call for bridging the scales from genes to behavior, but rather stresses the unifying perspective offered by the concepts referred to in the title. It is believed that the interdisciplinary approach adopted here will be beneficial for all the above mentioned fields.
Download or read book Handbook of Geomathematics written by Willi Freeden and published by Springer Science & Business Media. This book was released on 2010-08-13 with total page 1371 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the last three decades geosciences and geo-engineering were influenced by two essential scenarios: First, the technological progress has changed completely the observational and measurement techniques. Modern high speed computers and satellite based techniques are entering more and more all geodisciplines. Second, there is a growing public concern about the future of our planet, its climate, its environment, and about an expected shortage of natural resources. Obviously, both aspects, viz. efficient strategies of protection against threats of a changing Earth and the exceptional situation of getting terrestrial, airborne as well as spaceborne data of better and better quality explain the strong need of new mathematical structures, tools, and methods. Mathematics concerned with geoscientific problems, i.e., Geomathematics, is becoming increasingly important. The ‘Handbook Geomathematics’ as a central reference work in this area comprises the following scientific fields: (I) observational and measurement key technologies (II) modelling of the system Earth (geosphere, cryosphere, hydrosphere, atmosphere, biosphere) (III) analytic, algebraic, and operator-theoretic methods (IV) statistical and stochastic methods (V) computational and numerical analysis methods (VI) historical background and future perspectives.
Download or read book Mathematical Reviews written by and published by . This book was released on 2005 with total page 1884 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Frames for Undergraduates written by Deguang Han and published by American Mathematical Soc.. This book was released on 2007 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The early chapters contain the topics from linear algebra that students need to know in order to read the rest of the book. The later chapters are devoted to advanced topics, which allow students with more experience to study more intricate types of frames. Toward that end, a Student Presentation section gives detailed proofs of fairly technical results with the intention that a student could work out these proofs independently and prepare a presentation to a class or research group. The authors have also presented some stories in the Anecdotes section about how this material has motivated and influenced their students."--BOOK JACKET.
Download or read book Finite Frames written by Peter G. Casazza and published by Springer Science & Business Media. This book was released on 2012-09-14 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 monograph has yet appeared on the subject. Edited by two of the leading experts in the field, Finite Frames aims to fill this void in the literature by providing a comprehensive, systematic study of finite frame theory and applications. With carefully selected contributions written by highly experienced researchers, it covers topics including: * Finite Frame Constructions; * Optimal Erasure Resilient Frames; * Quantization of Finite Frames; * Finite Frames and Compressed Sensing; * Group and Gabor Frames; * Fusion Frames. Despite the variety of its chapters' source and content, the book's notation and terminology are unified throughout and provide a definitive picture of the current state of frame theory. With a broad range of applications and a clear, full presentation, this book is a highly valuable resource for graduate students and researchers across disciplines such as applied harmonic analysis, electrical engineering, quantum computing, medicine, and more. It is designed to be used as a supplemental textbook, self-study guide, or reference book.
