Distributions, Partial Differential Equations, and Harmonic Analysis

Nonfiction, Science & Nature, Mathematics, Functional Analysis, Differential Equations
Cover of the book Distributions, Partial Differential Equations, and Harmonic Analysis by Dorina Mitrea, Springer International Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Dorina Mitrea ISBN: 9783030032968
Publisher: Springer International Publishing Publication: December 29, 2018
Imprint: Springer Language: English
Author: Dorina Mitrea
ISBN: 9783030032968
Publisher: Springer International Publishing
Publication: December 29, 2018
Imprint: Springer
Language: English

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). 

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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). 

More books from Springer International Publishing

Cover of the book La phénoménologie génétique de Marc Richir by Dorina Mitrea
Cover of the book Sustainable Intensification to Advance Food Security and Enhance Climate Resilience in Africa by Dorina Mitrea
Cover of the book A Systems Biology Approach to Study Metabolic Syndrome by Dorina Mitrea
Cover of the book Buildings for Advanced Technology by Dorina Mitrea
Cover of the book Hearing Aids by Dorina Mitrea
Cover of the book MIMO Radar Waveform Design for Spectrum Sharing with Cellular Systems by Dorina Mitrea
Cover of the book New Perspectives on Internationalization and Competitiveness by Dorina Mitrea
Cover of the book Competing Structures in the Bilingual Mind by Dorina Mitrea
Cover of the book Provocative Screens by Dorina Mitrea
Cover of the book Endophytes of Forest Trees by Dorina Mitrea
Cover of the book Changing Paradigms in the Management of Breast Cancer by Dorina Mitrea
Cover of the book Endophthalmitis by Dorina Mitrea
Cover of the book Medical Image Computing and Computer Assisted Intervention − MICCAI 2017 by Dorina Mitrea
Cover of the book Euclidean Geometry and its Subgeometries by Dorina Mitrea
Cover of the book Women, Religion, and the Gift by Dorina Mitrea
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy