LEADER 03784nam 2200661 450 001 9910797203403321 005 20230807221010.0 010 $a0-19-104783-X 010 $a0-19-179771-5 010 $a0-19-104782-1 035 $a(CKB)3710000000442359 035 $a(EBL)2101599 035 $a(SSID)ssj0001560717 035 $a(PQKBManifestationID)16193856 035 $a(PQKBTitleCode)TC0001560717 035 $a(PQKBWorkID)14825531 035 $a(PQKB)11652967 035 $a(StDuBDS)EDZ0001199407 035 $a(MiAaPQ)EBC2101599 035 $a(Au-PeEL)EBL2101599 035 $a(CaPaEBR)ebr11074252 035 $a(CaONFJC)MIL811208 035 $a(OCoLC)915311273 035 $a(MiAaPQ)EBC4700480 035 $a(EXLCZ)993710000000442359 100 $a20150714h20152015 uy 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aFunction spaces and partial differential equations$hVolume 1$iClassical analysis /$fAli Taheri 205 $aFirst edition. 210 1$aOxford, England :$cOxford University Press,$d2015. 210 4$dİ2015 215 $a1 online resource (523 p.) 225 1 $aOxford Lecture Series in Mathematics and Its Applications 300 $aDescription based upon print version of record. 311 $a0-19-873313-5 320 $aIncludes bibliographical references and index. 327 $aCover; Preface; Contents of Volume 1; Contents of Volume 2; 1 Harmonic Functions and the Mean-Value Property; 1.1 Spherical Means; 1.2 Mean-Value Property and Smoothness; 1.3 Maximum Principles; 1.4 The Laplace-Beltrami Operator on Spheres; 1.5 Harnack's Monotone Convergence Theorem; 1.6 Interior Estimates and Uniform Gradient Bounds; 1.7 Weyl's Lemma on Weakly Harmonic Functions; 1.8 Exercises and Further Results; 2 Poisson Kernels and Green's Representation Formula; 2.1 The Fundamental Solution N of ?; 2.2 Green's Identities and Representation Formulas; 2.3 The Green's Function G = G(x,y 327 $a?)2.4 The Poisson Kernel P = P(x,y; ?); 2.5 Explicit Constructions: Balls; 2.6 Explicit Constructions: Half-Spaces; 2.7 The Newtonian Potential N[f; ?]; 2.8 Decay of the Newtonian Potential; 2.9 Second Order Derivatives and ?N[f; ?]; 2.10 Exercises and Further Results; 3 Abel-Poisson and Feje?r Means of Fourier Series; 3.1 Function Spaces on the Circle; 3.2 Conjugate Series; Magnitude of Fourier Coefficients; 3.3 Summability Methods; Tauberian Theorems; 3.4 Abel-Poisson vs. Feje?r Means of Fourier Series; 3.5 L1(T) and M(T) as Convolution Banach Algebras 327 $a6.10 Exercises and Further Results 330 $aThis is a book written primarily for graduate students and early researchers in the fields of Analysis and Partial Differential Equations (PDEs). Coverage of the material is essentially self-contained, extensive and novel with great attention to details and rigour. The strength of the book primarily lies in its clear and detailed explanations, scope and coverage, highlighting and presenting deep and profound inter-connections between different related and seeminglyunrelated disciplines within classical and modern mathematics and above all the extensive collection of examples, worked-out and hi 410 0$aOxford lecture series in mathematics and its applications. 606 $aFunction spaces 606 $aDifferential equations, Partial 615 0$aFunction spaces. 615 0$aDifferential equations, Partial. 676 $a515.73 700 $aTaheri$b Ali$01504051 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910797203403321 996 $aFunction spaces and partial differential equations$93732826 997 $aUNINA