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Titlebook: Distributions, Partial Differential Equations, and Harmonic Analysis; Dorina Mitrea Textbook 2018Latest edition Springer Nature Switzerlan

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书目名称Distributions, Partial Differential Equations, and Harmonic Analysis
编辑Dorina Mitrea
视频video
概述Pursues the development of distribution theory simultaneously with relevant incursions into partial differential equations and harmonic analysis.Written in a concise, rigorous, and largely self-contai
丛书名称Universitext
图书封面Titlebook: Distributions, Partial Differential Equations, and Harmonic Analysis;  Dorina Mitrea Textbook 2018Latest edition Springer Nature Switzerlan
描述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-studyguide. 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 technica
出版日期Textbook 2018Latest edition
关键词Distributions; Fourier Analysis; Fundamental Solutions; Partial Diffential Equations texbook; Potential
版次2
doihttps://doi.org/10.1007/978-3-030-03296-8
isbn_softcover978-3-030-03295-1
isbn_ebook978-3-030-03296-8Series ISSN 0172-5939 Series E-ISSN 2191-6675
issn_series 0172-5939
copyrightSpringer Nature Switzerland AG 2018
The information of publication is updating

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https://doi.org/10.1007/978-1-4612-4250-5ain, both these brands of Sobolev spaces (defined intrinsically and via restriction) coincide for an integer amount of smoothness. A key role in the proof of this result is played by Calderón’s extension operator, mapping functions originally defined in the said Lipschitz domain to the entire Euclid
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Textbook 2018Latest edition of mathematical interests will find this book to be a useful resource and complete self-studyguide. 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 technica
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Weak Derivatives,duced as a mean of extending the notion of solution to a more general setting, where the functions involved may lack standard pointwise differentiability properties. Here two classes of test functions are also defined and discussed.
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The Laplacian and Related Operators,er. While the natural starting point is the Laplacian, this study encompasses a variety of related operators, such as the bi-Laplacian, the poly-harmonic operator, the Helmholtz operator and its iterations, the Cauchy–Riemann operator, the Dirac operator, the perturbed Dirac operator and its iterati
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