000			02906nam a22002777a 4500
999			_c55793 _d55793
005			20191022125352.0
008			191022b ||||| |||| 00| 0 eng d
020			_a9781470454739
082			_a515.7 HAA
100			_aHaase, Markus
245			_a Functional analysis _b : an elementary introduction _c/ Markus Haase
260			_aProvidence, Rhode Island _b: American Mathematical Society, _c©2014
300			_axviii, 372 pages _c; 26 cm
490			_aGraduate studies in mathematics, v. 156.
505			_a 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.
520			_a 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
650			_aMathematics
650			_aAnalysis
650			_aFunctional analysis --
650			_aDifferential equations, Partial.
650			_aFunctional analysis -- Instructional exposition (textbooks, tutorial papers, etc.)
650			_aPartial differential equations -- Spectral theory and eigenvalue problems -- Spectral theory and eigenvalue problems.
650			_aDifferentialekvationer -- läromedel.
700			_aHaase, Markus
942			_cMDL