04529nam 22008773 450 991096301930332120250520153456.09780191047831019104783X9780191797712019179771597801910478240191047821(PPN)28092741X(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(MiAaPQ)EBC31355573(Au-PeEL)EBL31355573(OCoLC)913576111(FINmELB)ELB161879(EXLCZ)99371000000044235920240709d2015 uy 0engur|n|---|||||txtccrFunction spaces and partial differential equationsVolume 2Contemporary analysis /Ali Taheri, Department of Mathematics, University of SussexFirst edition.Oxford, United Kingdom :Oxford University Press,2015.©20151 online resource (523 p.)Oxford lecture series in mathematics and its applications ;Volume 40-41Description based upon print version of record.9780198733133 0198733135 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 ;Volume 40-41.Differential equations, PartialFunction spacesMathematical analysisEquacions en derivades parcialsthubEspais funcionalsthubAnàlisi matemàticathubLlibres electrònicsthubDifferential equations, Partial.Function spaces.Mathematical analysis.Equacions en derivades parcialsEspais funcionalsAnàlisi matemàtica515.353Taheri Ali1694806MiAaPQMiAaPQMiAaPQBOOK9910963019303321Function spaces and partial differential equations4073590UNINA