Modulation Spaces
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| Author | : Árpád Bényi |
| Publisher | : Springer Nature |
| Total Pages | : 177 |
| Release | : 2020-02-22 |
| Genre | : Mathematics |
| ISBN | : 1071603329 |
This monograph serves as a much-needed, self-contained reference on the topic of modulation spaces. By gathering together state-of-the-art developments and previously unexplored applications, readers will be motivated to make effective use of this topic in future research. Because modulation spaces have historically only received a cursory treatment, this book will fill a gap in time-frequency analysis literature, and offer readers a convenient and timely resource. Foundational concepts and definitions in functional, harmonic, and real analysis are reviewed in the first chapter, which is then followed by introducing modulation spaces. The focus then expands to the many valuable applications of modulation spaces, such as linear and multilinear pseudodifferential operators, and dispersive partial differential equations. Because it is almost entirely self-contained, these insights will be accessible to a wide audience of interested readers. Modulation Spaces will be an ideal reference for researchers in time-frequency analysis and nonlinear partial differential equations. It will also appeal to graduate students and seasoned researchers who seek an introduction to the time-frequency analysis of nonlinear dispersive partial differential equations.
| Author | : Raed Mesleh |
| Publisher | : John Wiley & Sons |
| Total Pages | : 284 |
| Release | : 2018-06-19 |
| Genre | : Technology & Engineering |
| ISBN | : 1119375657 |
Explores the fundamentals required to understand, analyze, and implement space modulation techniques (SMTs) in coherent and non-coherent radio frequency environments This book focuses on the concept of space modulation techniques (SMTs), and covers those emerging high data rate wireless communication techniques. The book discusses the advantages and disadvantages of SMTs along with their performance. A general framework for analyzing the performance of SMTs is provided and used to detail their performance over several generalized fading channels. The book also addresses the transmitter design of these techniques with the optimum number of hardware components and the use of these techniques in cooperative and mm-Wave communications. Beginning with an introduction to the subject and a brief history, Space Modulation Techniques goes on to offer chapters covering MIMO systems like spatial multiplexing and space-time coding. It then looks at channel models, such as Rayleigh, Rician, Nakagami-m, and other generalized distributions. A discussion of SMTs includes techniques like space shift keying (SSK), space-time shift keying (STSK), trellis coded spatial modulation (TCSM), spatial modulation (SM), generalized spatial modulation (GSM), quadrature spatial modulation (QSM), and more. The book also presents a non-coherent design for different SMTs, and a framework for SMTs’ performance analysis in different channel conditions and in the presence of channel imperfections, all that along with an information theoretic treatment of SMTs. Lastly, it provides performance comparisons, results, and MATLAB codes and offers readers practical implementation designs for SMTs. The book also: Provides readers with the expertise of the inventors of space modulation techniques (SMTs) Analyzes error performance, capacity performance, and system complexity. Discusses practical implementation of SMTs and studies SMTs with cooperative and mm-Wave communications Explores and compares MIMO schemes Space Modulation Techniques is an ideal book for professional and academic readers that are active in the field of SMT MIMO systems.
| Author | : Christopher Heil |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 390 |
| Release | : 2007-08-02 |
| Genre | : Mathematics |
| ISBN | : 0817645047 |
This self-contained volume in honor of John J. Benedetto covers a wide range of topics in harmonic analysis and related areas. These include weighted-norm inequalities, frame theory, wavelet theory, time-frequency analysis, and sampling theory. The chapters are clustered by topic to provide authoritative expositions that will be of lasting interest. The original papers collected are written by prominent researchers and professionals in the field. The book pays tribute to John J. Benedetto’s achievements and expresses an appreciation for the mathematical and personal inspiration he has given to so many students, co-authors, and colleagues.
| Author | : Yoshihiro Sawano |
| Publisher | : Springer |
| Total Pages | : 964 |
| Release | : 2018-11-04 |
| Genre | : Mathematics |
| ISBN | : 9811308365 |
This is a self-contained textbook of the theory of Besov spaces and Triebel–Lizorkin spaces oriented toward applications to partial differential equations and problems of harmonic analysis. These include a priori estimates of elliptic differential equations, the T1 theorem, pseudo-differential operators, the generator of semi-group and spaces on domains, and the Kato problem. Various function spaces are introduced to overcome the shortcomings of Besov spaces and Triebel–Lizorkin spaces as well. The only prior knowledge required of readers is familiarity with integration theory and some elementary functional analysis.Illustrations are included to show the complicated way in which spaces are defined. Owing to that complexity, many definitions are required. The necessary terminology is provided at the outset, and the theory of distributions, L^p spaces, the Hardy–Littlewood maximal operator, and the singular integral operators are called upon. One of the highlights is that the proof of the Sobolev embedding theorem is extremely simple. There are two types for each function space: a homogeneous one and an inhomogeneous one. The theory of function spaces, which readers usually learn in a standard course, can be readily applied to the inhomogeneous one. However, that theory is not sufficient for a homogeneous space; it needs to be reinforced with some knowledge of the theory of distributions. This topic, however subtle, is also covered within this volume. Additionally, related function spaces—Hardy spaces, bounded mean oscillation spaces, and Hölder continuous spaces—are defined and discussed, and it is shown that they are special cases of Besov spaces and Triebel–Lizorkin spaces.
| Author | : Karlheinz Gröchenig |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 367 |
| Release | : 2013-12-01 |
| Genre | : Technology & Engineering |
| ISBN | : 1461200032 |
Time-frequency analysis is a modern branch of harmonic analysis. It com prises all those parts of mathematics and its applications that use the struc ture of translations and modulations (or time-frequency shifts) for the anal ysis of functions and operators. Time-frequency analysis is a form of local Fourier analysis that treats time and frequency simultaneously and sym metrically. My goal is a systematic exposition of the foundations of time-frequency analysis, whence the title of the book. The topics range from the elemen tary theory of the short-time Fourier transform and classical results about the Wigner distribution via the recent theory of Gabor frames to quantita tive methods in time-frequency analysis and the theory of pseudodifferential operators. This book is motivated by applications in signal analysis and quantum mechanics, but it is not about these applications. The main ori entation is toward the detailed mathematical investigation of the rich and elegant structures underlying time-frequency analysis. Time-frequency analysis originates in the early development of quantum mechanics by H. Weyl, E. Wigner, and J. von Neumann around 1930, and in the theoretical foundation of information theory and signal analysis by D.
| Author | : Felix Voigtlaender |
| Publisher | : American Mathematical Society |
| Total Pages | : 268 |
| Release | : 2023-07-31 |
| Genre | : Mathematics |
| ISBN | : 1470459906 |
View the abstract. https://www.ams.org/bookstore/pspdf/memo-287-1426-abstract.pdf
| Author | : Radu Balan |
| Publisher | : Birkhäuser |
| Total Pages | : 440 |
| Release | : 2015-10-20 |
| Genre | : Mathematics |
| ISBN | : 3319201883 |
This volume consists of contributions spanning a wide spectrum of harmonic analysis and its applications written by speakers at the February Fourier Talks from 2002 – 2013. Containing cutting-edge results by an impressive array of mathematicians, engineers and scientists in academia, industry and government, it will be an excellent reference for graduate students, researchers and professionals in pure and applied mathematics, physics and engineering. Topics covered include: Special Topics in Harmonic Analysis Applications and Algorithms in the Physical Sciences Gabor Theory RADAR and Communications: Design, Theory, and Applications The February Fourier Talks are held annually at the Norbert Wiener Center for Harmonic Analysis and Applications. Located at the University of Maryland, College Park, the Norbert Wiener Center provides a state-of- the-art research venue for the broad emerging area of mathematical engineering.
| Author | : Joachim Toft |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 338 |
| Release | : 2007-01-22 |
| Genre | : Mathematics |
| ISBN | : 3764380977 |
The ISAAC Group in Pseudo-Differential Operators (IGPDO) met at the Fifth ISAAC Congress held at Università di Catania in Italy in July, 2005. This volume consists of papers based on lectures given at the special session on pseudodifferential operators and invited papers that bear on the themes of IGPDO. Nineteen peer-reviewed papers represent modern trends in pseudo-differential operators. Diverse topics related to pseudo-differential operators are covered.
| Author | : Ole Christensen |
| Publisher | : Birkhäuser |
| Total Pages | : 719 |
| Release | : 2016-05-24 |
| Genre | : Mathematics |
| ISBN | : 3319256130 |
This revised and expanded monograph presents the general theory for frames and Riesz bases in Hilbert spaces as well as its concrete realizations within Gabor analysis, wavelet analysis, and generalized shift-invariant systems. Compared with the first edition, more emphasis is put on explicit constructions with attractive properties. Based on the exiting development of frame theory over the last decade, this second edition now includes new sections on the rapidly growing fields of LCA groups, generalized shift-invariant systems, duality theory for as well Gabor frames as wavelet frames, and open problems in the field. Key features include: *Elementary introduction to frame theory in finite-dimensional spaces * Basic results presented in an accessible way for both pure and applied mathematicians * Extensive exercises make the work suitable as a textbook for use in graduate courses * Full proofs includ ed in introductory chapters; only basic knowledge of functional analysis required * Explicit constructions of frames and dual pairs of frames, with applications and connections to time-frequency analysis, wavelets, and generalized shift-invariant systems * Discussion of frames on LCA groups and the concrete realizations in terms of Gabor systems on the elementary groups; connections to sampling theory * Selected research topics presented with recommendations for more advanced topics and further readin g * Open problems to stimulate further research An Introduction to Frames and Riesz Bases will be of interest to graduate students and researchers working in pure and applied mathematics, mathematical physics, and engineering. Professionals working in digital signal processing who wish to understand the theory behind many modern signal processing tools may also find this book a useful self-study reference. Review of the first edition: "Ole Christensen’s An Introduction to Frames and Riesz Bases is a first-rate introduction to the field ... . The book provides an excellent exposition of these topics. The material is broad enough to pique the interest of many readers, the included exercises supply some interesting challenges, and the coverage provides enough background for those new to the subject to begin conducting original research." — Eric S. Weber, American Mathematical Monthly, Vol. 112, February, 2005
| Author | : Michael Ruzhansky |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 416 |
| Release | : 2014-01-18 |
| Genre | : Mathematics |
| ISBN | : 3319025503 |
This book is devoted to the broad field of Fourier analysis and its applications to several areas of mathematics, including problems in the theory of pseudo-differential operators, partial differential equations, and time-frequency analysis. It is based on lectures given at the international conference “Fourier Analysis and Pseudo-Differential Operators,” June 25–30, 2012, at Aalto University, Finland. This collection of 20 refereed articles is based on selected talks and presents the latest advances in the field. The conference was a satellite meeting of the 6th European Congress of Mathematics, which took place in Krakow in July 2012; it was also the 6th meeting in the series “Fourier Analysis and Partial Differential Equations.”
