Distributions Partial Differential Equations And Harmonic Analysis
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Author |
: Dorina Mitrea |
Publisher |
: Springer |
Total Pages |
: 600 |
Release |
: 2018-12-29 |
ISBN-10 |
: 9783030032968 |
ISBN-13 |
: 3030032965 |
Rating |
: 4/5 (68 Downloads) |
Synopsis Distributions, Partial Differential Equations, and Harmonic Analysis by : Dorina Mitrea
The aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity. The main additions to the current, second edition, pertain to fundamental solutions (through the inclusion of the Helmholtz operator, the perturbed Dirac operator, and their iterations) and the theory of Sobolev spaces (built systematically from the ground up, exploiting natural connections with the Fourier Analysis developed earlier in the monograph).
Author |
: Vladimir Georgiev |
Publisher |
: Springer Nature |
Total Pages |
: 317 |
Release |
: 2020-11-07 |
ISBN-10 |
: 9783030582159 |
ISBN-13 |
: 3030582159 |
Rating |
: 4/5 (59 Downloads) |
Synopsis Advances in Harmonic Analysis and Partial Differential Equations by : Vladimir Georgiev
This book originates from the session "Harmonic Analysis and Partial Differential Equations" held at the 12th ISAAC Congress in Aveiro, and provides a quick overview over recent advances in partial differential equations with a particular focus on the interplay between tools from harmonic analysis, functional inequalities and variational characterisations of solutions to particular non-linear PDEs. It can serve as a useful source of information to mathematicians, scientists and engineers. The volume contains contributions of authors from a variety of countries on a wide range of active research areas covering different aspects of partial differential equations interacting with harmonic analysis and provides a state-of-the-art overview over ongoing research in the field. It shows original research in full detail allowing researchers as well as students to grasp new aspects and broaden their understanding of the area.
Author |
: Svetlin G. Georgiev |
Publisher |
: Springer Nature |
Total Pages |
: 270 |
Release |
: 2021-08-21 |
ISBN-10 |
: 9783030812652 |
ISBN-13 |
: 3030812650 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Theory of Distributions by : Svetlin G. Georgiev
This book explains many fundamental ideas on the theory of distributions. The theory of partial differential equations is one of the synthetic branches of analysis that combines ideas and methods from different fields of mathematics, ranging from functional analysis and harmonic analysis to differential geometry and topology. This presents specific difficulties to those studying this field. This second edition, which consists of 10 chapters, is suitable for upper undergraduate/graduate students and mathematicians seeking an accessible introduction to some aspects of the theory of distributions. It can also be used for one-semester course.
Author |
: Lars Hörmander |
Publisher |
: Springer |
Total Pages |
: 454 |
Release |
: 2015-03-30 |
ISBN-10 |
: 9783642614972 |
ISBN-13 |
: 3642614973 |
Rating |
: 4/5 (72 Downloads) |
Synopsis The Analysis of Linear Partial Differential Operators I by : Lars Hörmander
The main change in this edition is the inclusion of exercises with answers and hints. This is meant to emphasize that this volume has been written as a general course in modern analysis on a graduate student level and not only as the beginning of a specialized course in partial differen tial equations. In particular, it could also serve as an introduction to harmonic analysis. Exercises are given primarily to the sections of gen eral interest; there are none to the last two chapters. Most of the exercises are just routine problems meant to give some familiarity with standard use of the tools introduced in the text. Others are extensions of the theory presented there. As a rule rather complete though brief solutions are then given in the answers and hints. To a large extent the exercises have been taken over from courses or examinations given by Anders Melin or myself at the University of Lund. I am grateful to Anders Melin for letting me use the problems originating from him and for numerous valuable comments on this collection. As in the revised printing of Volume II, a number of minor flaws have also been corrected in this edition. Many of these have been called to my attention by the Russian translators of the first edition, and I wish to thank them for our excellent collaboration.
Author |
: C. Zuily |
Publisher |
: Elsevier |
Total Pages |
: 247 |
Release |
: 1988-04-01 |
ISBN-10 |
: 9780080872544 |
ISBN-13 |
: 0080872549 |
Rating |
: 4/5 (44 Downloads) |
Synopsis Problems in Distributions and Partial Differential Equations by : C. Zuily
The aim of this book is to provide a comprehensive introduction to the theory of distributions, by the use of solved problems. Although written for mathematicians, it can also be used by a wider audience, including engineers and physicists.The first six chapters deal with the classical theory, with special emphasis on the concrete aspects. The reader will find many examples of distributions and learn how to work with them. At the beginning of each chapter the relevant theoretical material is briefly recalled. The last chapter is a short introduction to a very wide and important field in analysis which can be considered as the most natural application of distributions, namely the theory of partial differential equations. It includes exercises on the classical differential operators and on fundamental solutions, hypoellipticity, analytic hypoellipticity, Sobolev spaces, local solvability, the Cauchy problem, etc.
Author |
: Robert S Strichartz |
Publisher |
: World Scientific Publishing Company |
Total Pages |
: 238 |
Release |
: 2003-06-13 |
ISBN-10 |
: 9789813102293 |
ISBN-13 |
: 9813102292 |
Rating |
: 4/5 (93 Downloads) |
Synopsis A Guide To Distribution Theory And Fourier Transforms by : Robert S Strichartz
This important book provides a concise exposition of the basic ideas of the theory of distribution and Fourier transforms and its application to partial differential equations. The author clearly presents the ideas, precise statements of theorems, and explanations of ideas behind the proofs. Methods in which techniques are used in applications are illustrated, and many problems are included. The book also introduces several significant recent topics, including pseudodifferential operators, wave front sets, wavelets, and quasicrystals. Background mathematical prerequisites have been kept to a minimum, with only a knowledge of multidimensional calculus and basic complex variables needed to fully understand the concepts in the book.A Guide to Distribution Theory and Fourier Transforms can serve as a textbook for parts of a course on Applied Analysis or Methods of Mathematical Physics, and in fact it is used that way at Cornell.
Author |
: J.J. Duistermaat |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 455 |
Release |
: 2010-08-09 |
ISBN-10 |
: 9780817646752 |
ISBN-13 |
: 0817646752 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Distributions by : J.J. Duistermaat
This textbook is an application-oriented introduction to the theory of distributions, a powerful tool used in mathematical analysis. The treatment emphasizes applications that relate distributions to linear partial differential equations and Fourier analysis problems found in mechanics, optics, quantum mechanics, quantum field theory, and signal analysis. The book is motivated by many exercises, hints, and solutions that guide the reader along a path requiring only a minimal mathematical background.
Author |
: Alexander I. Saichev |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 427 |
Release |
: 2013-09-05 |
ISBN-10 |
: 9780817646523 |
ISBN-13 |
: 0817646523 |
Rating |
: 4/5 (23 Downloads) |
Synopsis Distributions in the Physical and Engineering Sciences, Volume 2 by : Alexander I. Saichev
Distributions in the Physical and Engineering Sciences is a comprehensive exposition on analytic methods for solving science and engineering problems. It is written from the unifying viewpoint of distribution theory and enriched with many modern topics which are important for practitioners and researchers. The goal of the books is to give the reader, specialist and non-specialist, useable and modern mathematical tools in their research and analysis. Volume 2: Linear and Nonlinear Dynamics of Continuous Media continues the multivolume project which endeavors to show how the theory of distributions, also called the theory of generalized functions, can be used by graduate students and researchers in applied mathematics, physical sciences, and engineering. It contains an analysis of the three basic types of linear partial differential equations--elliptic, parabolic, and hyperbolic--as well as chapters on first-order nonlinear partial differential equations and conservation laws, and generalized solutions of first-order nonlinear PDEs. Nonlinear wave, growing interface, and Burger’s equations, KdV equations, and the equations of gas dynamics and porous media are also covered. The careful explanations, accessible writing style, many illustrations/examples and solutions also make it suitable for use as a self-study reference by anyone seeking greater understanding and proficiency in the problem solving methods presented. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. Features · Application oriented exposition of distributional (Dirac delta) methods in the theory of partial differential equations. Abstract formalism is keep to a minimum. · Careful and rich selection of examples and problems arising in real-life situations. Complete solutions to all exercises appear at the end of the book. · Clear explanations, motivations, and illustration of all necessary mathematical concepts.
Author |
: Adina Chirilă |
Publisher |
: Springer Nature |
Total Pages |
: 277 |
Release |
: 2021-02-08 |
ISBN-10 |
: 9783030671594 |
ISBN-13 |
: 3030671593 |
Rating |
: 4/5 (94 Downloads) |
Synopsis Distribution Theory Applied to Differential Equations by : Adina Chirilă
This book presents important contributions to modern theories concerning the distribution theory applied to convex analysis (convex functions, functions of lower semicontinuity, the subdifferential of a convex function). The authors prove several basic results in distribution theory and present ordinary differential equations and partial differential equations by providing generalized solutions. In addition, the book deals with Sobolev spaces, which presents aspects related to variation problems, such as the Stokes system, the elasticity system and the plate equation. The authors also include approximate formulations of variation problems, such as the Galerkin method or the finite element method. The book is accessible to all scientists, and it is especially useful for those who use mathematics to solve engineering and physics problems. The authors have avoided concepts and results contained in other books in order to keep the book comprehensive. Furthermore, they do not present concrete simplified models and pay maximal attention to scientific rigor.
Author |
: Lars Hörmander |
Publisher |
: Springer My Copy UK |
Total Pages |
: 408 |
Release |
: 1983-05-01 |
ISBN-10 |
: 3642967515 |
ISBN-13 |
: 9783642967511 |
Rating |
: 4/5 (15 Downloads) |
Synopsis The analysis of linear partial differential operators by : Lars Hörmander