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Harmonic, Wavelet and P-Adic Analysis by N. M. Chuong Pdf
The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently. This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.
Harmonic, Wavelet and P-adic Analysis by Nguyen Minh Chuong Pdf
The mutual influence between mathematics and science and technology is becoming more and more widespread with profound connections among them being discovered. In particular, important connections between harmonic analysis, wavelet analysis and p-adic analysis have been found recently. This volume reports these findings and guides the reader towards the latest areas for further research. It is divided into two parts: harmonic, wavelet and p-adic analysis and p-adic and stochastic analysis.
Four Short Courses on Harmonic Analysis by Brigitte Forster,Peter Robert Massopust Pdf
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.
Pseudodifferential Operators and Wavelets over Real and p-adic Fields by Nguyen Minh Chuong Pdf
This monograph offers a self-contained introduction to pseudodifferential operators and wavelets over real and p-adic fields. Aimed at graduate students and researchers interested in harmonic analysis over local fields, the topics covered in this book include pseudodifferential operators of principal type and of variable order, semilinear degenerate pseudodifferential boundary value problems (BVPs), non-classical pseudodifferential BVPs, wavelets and Hardy spaces, wavelet integral operators, and wavelet solutions to Cauchy problems over the real field and the p-adic field.
Antieigenvalue Analysis by Karl Gustafson,Karl E. Gustafson Pdf
Karl Gustafson is the creater of the theory of antieigenvalue analysis. Its applications spread through fields as diverse as numerical analysis, wavelets, statistics, quantum mechanics, and finance. Antieigenvalue analysis, with its operator trigonometry, is a unifying language which enables new and deeper geometrical understanding of essentially every result in operator theory and matrix theory, together with their applications. This book will open up its methods to a wide range of specialists.
Wavelet Theory and Harmonic Analysis in Applied Sciences by Carlos E. D'Attellis,Elena M. Fernandez-Berdaguer Pdf
The idea of this book originated in the works presented at the First Latinamerican Conference on Mathematics in Industry and Medicine, held in Buenos Aires, Argentina, from November 27 to December 1, 1995. A variety of topics were discussed at this meeting. A large percentage of the papers focused on Wavelet and Harmonic Analysis. The theory and applications of this topic shown at the Conference were interesting enough to be published. Based on that we selected some works which make the core of this book. Other papers are contributions written by invited experts in the field to complete the presentation. All the works were written after the Conference. The purpose of this book is to present recent results as well as theo retical applied aspects of the subject. We have decided not to include a section devoted to the theoretical foundations of wavelet methods for non specialists. There are excellent introductions already available, for example, Chapter one in Wavelets in Medicine and Biology, edited by A. Aldroubi and M. Unser, 1996, or some of the references cited in the chapter.
Wavelet Analysis on Local Fields of Positive Characteristic by Biswaranjan Behera,Qaiser Jahan Pdf
This book discusses the theory of wavelets on local fields of positive characteristic. The discussion starts with a thorough introduction to topological groups and local fields. It then provides a proof of the existence and uniqueness of Haar measures on locally compact groups. It later gives several examples of locally compact groups and describes their Haar measures. The book focuses on multiresolution analysis and wavelets on a local field of positive characteristic. It provides characterizations of various functions associated with wavelet analysis such as scaling functions, wavelets, MRA-wavelets and low-pass filters. Many other concepts which are discussed in details are biorthogonal wavelets, wavelet packets, affine and quasi-affine frames, MSF multiwavelets, multiwavelet sets, generalized scaling sets, scaling sets, unconditional basis properties of wavelets and shift invariant spaces.
Analysis, Applications, and Computations by Uwe Kähler,Michael Reissig,Irene Sabadini,Jasson Vindas Pdf
This volume contains the contributions of the participants of the 13th International ISAAC Congress 2021, held in Ghent, Belgium. The papers, written by respected international experts, address recent results in mathematics, with a special focus on analysis. The volume provides to both specialists and non-specialists an excellent source of information on current research in mathematical analysis and its various interdisciplinary applications.
Infinite-dimensional Analysis: Operators In Hilbert Space; Stochastic Calculus Via Representations, And Duality Theory by Palle Jorgensen,James Tian Pdf
The purpose of this book is to make available to beginning graduate students, and to others, some core areas of analysis which serve as prerequisites for new developments in pure and applied areas. We begin with a presentation (Chapters 1 and 2) of a selection of topics from the theory of operators in Hilbert space, algebras of operators, and their corresponding spectral theory. This is a systematic presentation of interrelated topics from infinite-dimensional and non-commutative analysis; again, with view to applications. Chapter 3 covers a study of representations of the canonical commutation relations (CCRs); with emphasis on the requirements of infinite-dimensional calculus of variations, often referred to as Ito and Malliavin calculus, Chapters 4-6. This further connects to key areas in quantum physics.
Hardy Operators On Euclidean Spaces And Related Topics by Shanzhen Lu,Zunwei Fu,Fayou Zhao,Shaoguang Shi Pdf
In many branches of mathematical analysis and mathematical physics, the Hardy operator and Hardy inequality are fundamentally important and have been intensively studied ever since the pioneer researches. This volume presents new properties of higher-dimensional Hardy operators obtained by the authors and their collaborators over the last decade. Its prime focus is on higher-dimensional Hardy operators that are based on the spherical average form.The key motivation for this monograph is based on the fact that the Hardy operator is generally smaller than the Hardy-Littlewood maximal operator, which leads to, on the one hand, the operator norm of the Hardy operator itself being smaller than the latter. On the other hand, the former characterizing the weight function class or function spaces is greater than the latter.
Advances in Deterministic and Stochastic Analysis by Nguyen Minh Chuong Pdf
Trent Duncan did a good job holding his family together after his dad died. Hed kept his little sister out of trouble and taught her about life. Its just too bad he couldnt do the same for himself. Now hes the man your momma always warned you about: charming, smooth talking--and jobless. Hes got a phony business card and a line for every situation--and every conquest. But the ultimate player is about to play himself right outta the game. Because a couple of Trents ex-girlfriends are about to make him wish hed listened to his momma. . . The only person Trent cant seem to get around anymore is his big brother, Wil. Wils got problems of his own. He thought he was happily married, until his wife, Diane, stopped being intimate with him. Shes got her reasons, but if she doesnt explain herself soon, she may lose her husband to his voluptuous--and lusty--new secretary. Meanwhile, little sister Melanie is all grown up and sure shes met her prince--literally. Prince may be a friend of Trents, but the two men are like night and day. Prince is the kind of man Melanie would like to have kids with. Trouble is, shes not alone. Pretty soon, these three very different siblings have something in common--theyre all in hot water. And they need to find a way to help themselves--and each other--before they get burned. . .
Transmutation Operators and Applications by Vladislav V. Kravchenko,Sergei M. Sitnik Pdf
Transmutation operators in differential equations and spectral theory can be used to reveal the relations between different problems, and often make it possible to transform difficult problems into easier ones. Accordingly, they represent an important mathematical tool in the theory of inverse and scattering problems, of ordinary and partial differential equations, integral transforms and equations, special functions, harmonic analysis, potential theory, and generalized analytic functions. This volume explores recent advances in the construction and applications of transmutation operators, while also sharing some interesting historical notes on the subject.