000 03496nam a22005055i 4500
001 978-1-4614-8208-6
003 DE-He213
005 20140220082831.0
007 cr nn 008mamaa
008 130919s2013 xxu| s |||| 0|eng d
020 _a9781461482086
_9978-1-4614-8208-6
024 7 _a10.1007/978-1-4614-8208-6
_2doi
050 4 _aQA370-380
072 7 _aPBKJ
_2bicssc
072 7 _aMAT007000
_2bisacsh
082 0 4 _a515.353
_223
100 1 _aMitrea, Dorina.
_eauthor.
245 1 0 _aDistributions, Partial Differential Equations, and Harmonic Analysis
_h[electronic resource] /
_cby Dorina Mitrea.
264 1 _aNew York, NY :
_bSpringer New York :
_bImprint: Springer,
_c2013.
300 _aXXI, 460 p.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aUniversitext,
_x0172-5939
505 0 _aIntroduction -- Summary of Topological and Functional Analysis Results -- Weak Derivatives -- The Space D0() of Distributions -- The Fourier Transform -- The Space of Tempered Distributions -- Fundamental Solution -- The Laplace Operator -- The Heat Operator -- The Wave Operator -- The Lame Operator -- Fundamental Solutions for Other Operators -- Hypoelliptic operators -- Sobolev spaces -- Appendix -- References. .
520 _aThe 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.
650 0 _aMathematics.
650 0 _aFourier analysis.
650 0 _aFunctional analysis.
650 0 _aDifferential equations, partial.
650 0 _aPotential theory (Mathematics).
650 1 4 _aMathematics.
650 2 4 _aPartial Differential Equations.
650 2 4 _aFunctional Analysis.
650 2 4 _aFourier Analysis.
650 2 4 _aPotential Theory.
710 2 _aSpringerLink (Online service)
773 0 _tSpringer eBooks
776 0 8 _iPrinted edition:
_z9781461482079
830 0 _aUniversitext,
_x0172-5939
856 4 0 _uhttp://dx.doi.org/10.1007/978-1-4614-8208-6
912 _aZDB-2-SMA
999 _c96035
_d96035