Function spaces and partial differential equations . Volume 1 Classical analysis / / Ali Taheri

• Record Nr.: UNINA9910817463503321
• Autore: Taheri Ali
• Pubbl/distr/stampa: Oxford, England : , : Oxford University Press, , 2015; ©2015
• ISBN: 0-19-104783-X; 0-19-179771-5; 0-19-104782-1
• Edizione: [First edition.]
• Descrizione fisica: 1 online resource (523 p.)
• Collana: Oxford Lecture Series in Mathematics and Its Applications
• Disciplina: 515.73
• Soggetti: Function spaces; Differential equations, Partial
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: 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,y; Ω)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 Algebras; 6.10 Exercises and Further Results
• Sommario/riassunto: This 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