03784nam 2200661 450 991081746350332120230807221010.00-19-104783-X0-19-179771-50-19-104782-1(CKB)3710000000442359(EBL)2101599(SSID)ssj0001560717(PQKBManifestationID)16193856(PQKBTitleCode)TC0001560717(PQKBWorkID)14825531(PQKB)11652967(StDuBDS)EDZ0001199407(MiAaPQ)EBC2101599(Au-PeEL)EBL2101599(CaPaEBR)ebr11074252(CaONFJC)MIL811208(OCoLC)915311273(MiAaPQ)EBC4700480(EXLCZ)99371000000044235920150714h20152015 uy 0engur|n|---|||||txtccrFunction spaces and partial differential equationsVolume 1Classical analysis /Ali TaheriFirst edition.Oxford, England :Oxford University Press,2015.©20151 online resource (523 p.)Oxford Lecture Series in Mathematics and Its ApplicationsDescription based upon print version of record.0-19-873313-5 Includes bibliographical references and index.Cover; 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 Δ; 2.2 Green's Identities and Representation Formulas; 2.3 The Green's Function G = G(x,yΩ)2.4 The Poisson Kernel P = P(x,y; Ω); 2.5 Explicit Constructions: Balls; 2.6 Explicit Constructions: Half-Spaces; 2.7 The Newtonian Potential N[f; Ω]; 2.8 Decay of the Newtonian Potential; 2.9 Second Order Derivatives and ΔN[f; Ω]; 2.10 Exercises and Further Results; 3 Abel-Poisson and Fejér 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. Fejér Means of Fourier Series; 3.5 L1(T) and M(T) as Convolution Banach Algebras6.10 Exercises and Further ResultsThis 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 hiOxford lecture series in mathematics and its applications.Function spacesDifferential equations, PartialFunction spaces.Differential equations, Partial.515.73Taheri Ali1694806MiAaPQMiAaPQMiAaPQBOOK9910817463503321Function spaces and partial differential equations4073590UNINA