Frames and Other Bases in Abstract and Function Spaces: Novel Methods in Harmonic Analysis, Volume 1, Pesenson Isaac, Le Gia Quoc Thong, Mayeli Azita
Автор: Christensen Название: An Introduction to Frames and Riesz Bases ISBN: 3319256114 ISBN-13(EAN): 9783319256115 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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 included 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 reading* 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
Автор: Christensen Ole Название: An Introduction to Frames and Riesz Bases ISBN: 3319798146 ISBN-13(EAN): 9783319798141 Издательство: Springer Рейтинг: Цена: 11179.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Frames in Finite-dimensional Inner Product Spaces.- Infinite-dimensional Vector Spaces and Sequences.- Bases.- Bases and their Limitations.- Frames in Hilbert Spaces.- Tight Frames and Dual Frame Pairs.- Frames versus Riesz Bases.- Selected Topics in Frame Theory.- Frames of Translates.- Shift-Invariant Systems in l2(R).- Gabor Frames in L2(R).- Gabor Frames and Duality.- Selected Topics on Gabor Frames.- Gabor Frames in ℓ2(Z), L2(0, L), CL.- General Wavelet Frames in L2(R).- Dyadic Wavelet Frames for L2(R).- Frame Multiresolution Analysis.- Wavelet Frames via Extension Principles.- Selected Topics on Wavelet Frames.- Generalized Shift-Invariant Systems in L2(Rd).- Frames on Locally Compact Abelian Groups.- Perturbation of Frames.- Approximation of the Inverse Frame Operator.- Expansions in Banach Spaces. Append
Автор: Alexey Karapetyants; Vladislav Kravchenko; Elijah Название: Modern Methods in Operator Theory and Harmonic Analysis ISBN: 3030267474 ISBN-13(EAN): 9783030267476 Издательство: Springer Рейтинг: Цена: 20962.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
This proceedings volume gathers selected, peer-reviewed papers from the 'Modern Methods, Problems and Applications of Operator Theory and Harmonic Analysis VIII' (OTHA 2018) conference, which was held in Rostov-on-Don, Russia, in April 2018.The book covers a diverse range of topics in advanced mathematics, including harmonic analysis, functional analysis, operator theory, function theory, differential equations and fractional analysis – all fields that have been intensively developed in recent decades. Direct and inverse problems arising in mathematical physics are studied and new methods for solving them are presented. Complex multiparameter objects that require the involvement of operators with variable parameters and functional spaces, with fractional and even variable exponents, make these approaches all the more relevant.Given its scope, the book will especially benefit researchers with an interest in new trends in harmonic analysis and operator theory, though it will also appeal to graduate students seeking new and intriguing topics for further investigation.
Описание: This book offers an introduction to harmonic analysis on the simplest symmetric spaces. It places an emphasis on motivation, concrete examples, history, and, above all, applications in mathematics, statistics, physics, and engineering.
Автор: Isaac Pesenson; Quoc Thong Le Gia; Azita Mayeli; H Название: Frames and Other Bases in Abstract and Function Spaces ISBN: 3319555499 ISBN-13(EAN): 9783319555492 Издательство: Springer Рейтинг: Цена: 16769.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Frames: Theory and Practice.- Dynamical Sampling and Systems from Iterative Actions of Operators.- Optimization Methods for Frame Conditioning and Application to Graph Laplacian Scaling.- A Guide to Localized Frames and Applications to Galerkin-Like Representations of Operators.- Computing the Distance between Frames and between Subspaces of a Hilbert Space.- Sigma-Delta Quantization for Fusion Frames and Distributed Sensor Networks.- Recent Progress in Shearlet Theory: Systematic Construction of Shearlet Dilation Groups, Characterization of Wavefront Sets, and New Embeddings.- Numerical Solution to an Energy Concentration Problem Associated with the Special Affine Fourier Transformation.- A Frame Reconstruction Algorithm with Applications to Magnetic Resonance Imaging.- Frame Properties of Shifts of Prolate and Bandpass Prolate Functions.- Fast Fourier Transforms for Spherical Gauss-Laguerre Basis Functions.- Multiscale Radial Basis Functions.- Orthogonal Wavelet Frames on Manifolds Based on Conformal Mappings.- Quasi Monte Carlo Integration and Kernel-Based Function Approximation on Grassmannians.- Construction of Multiresolution Analysis Based on Localized Reproducing Kernels.- Regular Sampling on Metabelian Nilpotent Lie Groups: The Multiplicity-Free Case.- Parseval Space-Frequency Localized Frames on Sub-Riemann Compact Homogeneous Manifolds.
Автор: Ole Christensen Название: An Introduction to Frames and Riesz Bases ISBN: 1461265002 ISBN-13(EAN): 9781461265009 Издательство: Springer Рейтинг: Цена: 6986.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: The Applied and Numerical Harmonic Analysis ( ANHA) book series aims to provide the engineering, mathematical, and scientific communities with significant developments in harmonic analysis, ranging from abstract har- monic analysis to basic applications.
Описание: Introduction.- Characterization of Gevrey Regularity by a Class of FBI Transforms.- A Novel Mathematical Approach to the Theory of Translation Invariant Linear Systems.- Asymptotic Behaviour of the Fourier Transform of a Function of Bounded Variation.- Convergence and Regularization of Sampling Series.- Harmonic Analysis in Non-Euclidean Spaces: Theory and Application.- An Harmonic Analysis of Directed Graphs from Arithmetic Functions and Primes.- Sheaf and Duality Methods for Analyzing Multi-Model Systems.- On Boundary-Value Problems for a Partial Differential Equation with Caputo and Bessel Operator.- On the Solvability of the Zaremba Problem in Infinite Sectors and the Invertibility of Associated Singular Integral Operators.- On the Solution of the Oblique Derivative Problem by Constructive Runge-Walsh Concepts.- An Overview of Numerical Acceleration Techniques for Non-Linear Dimension Reduction.- Adaptive Density Estimation on the Circle by Nearly-Tight Frames.- Interactions between Kernels, Frames, and Persistent Homology.- Multi-Penalty Regularization for Detecting Relevant Variables.- Stable Likelihood Computation for Gaussian Random Fields.
Автор: Edwin Hewitt; Kenneth A. Ross Название: Abstract Harmonic Analysis ISBN: 3662245957 ISBN-13(EAN): 9783662245958 Издательство: Springer Рейтинг: Цена: 11878.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Readers who are interested only in compact groups may read as follows: 27, Appendix D, 28-30 [omitting subheads (30.6)-(30.60)ifdesired], (31.22)-(31.25), 32, 34-38, 44. Readers who are interested only in locally compact Abelian groups may read as follows: 31-33, 39-42, selected Mis- cellaneous Theorems and Examples in 34-38.
Автор: Folland, Gerald B. Название: Course in abstract harmonic analysis ISBN: 1498727131 ISBN-13(EAN): 9781498727136 Издательство: Taylor&Francis Рейтинг: Цена: 14086.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
A Course in Abstract Harmonic Analysis is an introduction to that part of analysis on locally compact groups that can be done with minimal assumptions on the nature of the group. As a generalization of classical Fourier analysis, this abstract theory creates a foundation for a great deal of modern analysis, and it contains a number of elegant results and techniques that are of interest in their own right.
This book develops the abstract theory along with a well-chosen selection of concrete examples that exemplify the results and show the breadth of their applicability. After a preliminary chapter containing the necessary background material on Banach algebras and spectral theory, the text sets out the general theory of locally compact groups and their unitary representations, followed by a development of the more specific theory of analysis on Abelian groups and compact groups. There is an extensive chapter on the theory of induced representations and its applications, and the book concludes with a more informal exposition on the theory of representations of non-Abelian, non-compact groups.
Featuring extensive updates and new examples, the Second Edition:
Adds a short section on von Neumann algebras
Includes Mark Kac's simple proof of a restricted form of Wiener's theorem
Explains the relation between SU(2) and SO(3) in terms of quaternions, an elegant method that brings SO(4) into the picture with little effort
Discusses representations of the discrete Heisenberg group and its central quotients, illustrating the Mackey machine for regular semi-direct products and the pathological phenomena for nonregular ones
A Course in Abstract Harmonic Analysis, Second Edition serves as an entr e to advanced mathematics, presenting the essentials of harmonic analysis on locally compact groups in a concise and accessible form.
Автор: Willi Freeden; M. Zuhair Nashed Название: Handbook of Mathematical Geodesy ISBN: 303009622X ISBN-13(EAN): 9783030096229 Издательство: Springer Рейтинг: Цена: 25155.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Written by leading experts, this book provides a clear and comprehensive survey of the “status quo” of the interrelating process and cross-fertilization of structures and methods in mathematical geodesy. Starting with a foundation of functional analysis, potential theory, constructive approximation, special function theory, and inverse problems, readers are subsequently introduced to today’s least squares approximation, spherical harmonics reflected spline and wavelet concepts, boundary value problems, Runge-Walsh framework, geodetic observables, geoidal modeling, ill-posed problems and regularizations, inverse gravimetry, and satellite gravity gradiometry. All chapters are self-contained and can be studied individually, making the book an ideal resource for both graduate students and active researchers who want to acquaint themselves with the mathematical aspects of modern geodesy.
Part I: Function Theory and Approximation Theory.- M. L. Goldman and E. Bakhtigareeva: Some General Properties of Operators in Morrey-type Spaces.- V. S. Guliyev, A. Eroglu and G. A. Abasova: Characterization of Parabolic Fractional Maximal Function and its Commutators in Orlicz Spaces.- A. Iosevich and K. Taylor: Finite Trees Inside Thin Subsets of Rd.- A. Karapetyants and J. E. Restrepo: Boundedness of Projection Operator in Generalized Holomorphic and Harmonic Spaces of Hцlder Type Functions.- K.S. Kazarian: Generalized Fourier Series by the Double Trigonometric System.- E. Liflyand: Hardy Type Inequalities in the Category of Hausdorff Operators.- H. R. Malonek, I. Caзгo, M. I. Falcгo and G. Tomaz: Harmonic Analysis and Hypercomplex Function Theory in Co-dimension One.- Y. Sawano: Paraproduct in Besov-Morrey Spaces.- Part II: Functional Analysis and Operator Theory.- E. I. Berezhnoĭ Analogs of the Khintchin - Kolmogorov Inequalities in Discrete Morrey Spaces.- R. Duduchava: Mellin Convolution Equations.- D. Hasanyan, A. Kamalyan, M. Karakhanyan & I. M. Spitkovsky: Integral Operators of the L-convolution Type in the Case of a Reflectionless Potential.- Y. Krasnov: Spectral Theory for Nonlinear Operators: Quadratic Case.- A. G. Kusraev and Z. A. Kusraeva: Factorization of Order Bounded Disjointness Preserving Multilinear Operators.- D. B. Rokhlin: Robbins-Monro Conditions for Persistent Exploration Learning Strategies.- E. Shulman: On Widths of Invariant Sets.- I. G. Tsar'kov: The Distance Function and Boundedness of Diameters of the Nearest Elements.- Part III: Differential Equations and Mathematical Physics.- H. S. Aslan and M. Reissig: The Influence of Oscillations on Energy Estimates for Damped Wave Models with Time-dependent Propagation Speed and Dissipation.- A. H. Babayan and S. H. Abelyan: On a Dirichlet Problem for One Improperly Elliptic Equation.- N. Gialelis and I. G. Stratis: On the 1-dim Defocusing NLS Equation with Non-vanishing Initial Data at Infinity.- Y. E. Gliklikh: On Time-global Solutions of SDE Having Nowhere Vanishing Initial Densities.- F. A. Gуmez and V. V. Kravchenko: On Transmutation Operators and Neumann Series of Bessel Functions Representations for Solutions of Linear Higher Order Differential Equations.- H.M. Hayrapetyan: On a Boundary Value Problem with Infinite Index.- O. Kudryavtsev and V. Rodochenko: A Numerical Realization of the Wiener-Hopf Method for the Kolmogorov Backward Equation.- A. Vatulyan and V. Yurov: On Waves Processes in Transversally-inhomogeneous Waveguides.- V. Yurko: Inverse Spectral Problems for Differential Systems.
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