LEADER 04476nam 22006135 450 001 9910303447003321 005 20200705123848.0 010 $a3-030-03296-5 024 7 $a10.1007/978-3-030-03296-8 035 $a(CKB)4100000007334954 035 $a(DE-He213)978-3-030-03296-8 035 $a(MiAaPQ)EBC6311746 035 $a(PPN)232964319 035 $a(EXLCZ)994100000007334954 100 $a20181229d2018 u| 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aDistributions, Partial Differential Equations, and Harmonic Analysis$b[electronic resource] /$fby Dorina Mitrea 205 $a2nd ed. 2018. 210 1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2018. 215 $a1 online resource (XXIII, 600 p. 1 illus.) 225 1 $aUniversitext,$x0172-5939 311 $a3-030-03295-7 327 $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. . 330 $aThe aim of this book is to offer, in a concise, rigorous, and largely self-contained manner, a rapid introduction to the theory of distributions and its applications to partial differential equations and harmonic analysis. The book is written in a format suitable for a graduate course spanning either over one-semester, when the focus is primarily on the foundational aspects, or over a two-semester period that allows for the proper amount of time to cover all intended applications as well. It presents a balanced treatment of the topics involved, and contains a large number of exercises (upwards of two hundred, more than half of which are accompanied by solutions), which have been carefully chosen to amplify the effect, and substantiate the power and scope, of the theory of distributions. Graduate students, professional mathematicians, and scientifically trained people with a wide spectrum of mathematical interests will find this book to be a useful resource and complete self-study guide. Throughout, a special effort has been made to develop the theory of distributions not as an abstract edifice but rather give the reader a chance to see the rationale behind various seemingly technical definitions, as well as the opportunity to apply the newly developed tools (in the natural build-up of the theory) to concrete problems in partial differential equations and harmonic analysis, at the earliest opportunity. The main additions to the current, second edition, pertain to fundamental solutions (through the inclusion of the Helmholtz operator, the perturbed Dirac operator, and their iterations) and the theory of Sobolev spaces (built systematically from the ground up, exploiting natural connections with the Fourier Analysis developed earlier in the monograph). . 410 0$aUniversitext,$x0172-5939 606 $aPartial differential equations 606 $aFunctional analysis 606 $aFourier analysis 606 $aPotential theory (Mathematics) 606 $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155 606 $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066 606 $aFourier Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12058 606 $aPotential Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M12163 615 0$aPartial differential equations. 615 0$aFunctional analysis. 615 0$aFourier analysis. 615 0$aPotential theory (Mathematics). 615 14$aPartial Differential Equations. 615 24$aFunctional Analysis. 615 24$aFourier Analysis. 615 24$aPotential Theory. 676 $a515.782 700 $aMitrea$b Dorina$4aut$4http://id.loc.gov/vocabulary/relators/aut$0521700 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910303447003321 996 $aDistributions, partial differential equations, and harmonic analysis$9837682 997 $aUNINA