02906nam a22002777a 4500 55792 55792 20191022125351.0 191022b ||||| |||| 00| 0 eng d 9781470454739 515.7 HAA Haase, Markus Functional analysis : an elementary introduction / Markus Haase Providence, Rhode Island : American Mathematical Society, ©2014 xviii, 372 pages ; 26 cm Graduate studies in mathematics, v. 156. Inner product spaces -- Normed spaces -- Distance and approximation -- Continuity and compactness -- Banach spaces -- *The Contraction Principle -- The Lebesgue spaces -- Hilbert Space Fundamentals -- Approximation Theory and Fourier Analysis -- Sobolev spaces and the Poisson Problem -- Operator Theory I -- Operator Theory II -- Spectral Theory of compact self-adjoint operators -- Applications of the Spectral Theorem -- Baire's Theorem and its consequences -- Duality and the Hahn-Banach Theorem -- Appendix A. Background -- Appendix B. The completion of a metric space -- Appendix C. Bernstein's proof of Weierstrass' Theorem -- Appendix D. Smooth cutoff functions -- Appendix E. Some topics from Fourier Analysis -- Appendix F. General Orthonormal systems. This book introduces functional analysis at an elementary level without assuming any background in real analysis, for example on metric spaces or Lebesgue integration. It focuses on concepts and methods relevant in applied contexts such as variational methods on Hilbert spaces, Neumann series, eigenvalue expansions for compact self-adjoint operators, weak differentiation and Sobolev spaces on intervals, and model applications to differential and integral equations. Beyond that, the final chapters on the uniform boundedness theorem, the open mapping theorem and the Hahn-Banach theorem provide a stepping-stone to more advanced texts. The exposition is clear and rigorous, featuring full and detailed proofs. Many examples illustrate the new notions and results. Each chapter concludes with a large collection of exercises, some of which are referred to in the margin of the text, tailor-made in order to guide the student digesting the new material. Optional sections and chapters supplement the mandatory parts and allow for modular teaching spanning from basic to honors track level. --Provided by publisher Mathematics Analysis Functional analysis -- Differential equations, Partial. Functional analysis -- Instructional exposition (textbooks, tutorial papers, etc.) Partial differential equations -- Spectral theory and eigenvalue problems -- Spectral theory and eigenvalue problems. Differentialekvationer -- läromedel. Haase, Markus MDL 0 0 ddc 0 0 MDL SNUL 2019-10-22 0 515.7 HAA M031 2019-10-22 00:00:00 2019-10-22 MDL