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FUNCTIONAL ANALYSIS Douglas N. Arnold References
This note covers the following topics: Vector spaces and their topology, Linear Operators and Functionals, The Open Mapping Theorem, Uniform Boundedness Principle, The Closed Range Theorem, Weak Topologies, Compact Operators and their Spectra, General Spectral Theory.
Author(s): Douglas N. Arnold
36 Pages 
This paper elaborates a short course on derivations and projections on Jordan triples. It introduces nonassociative algebra, continuous cohomology, and quantum functional analysis.
Author(s): Bernard Russo
72 Pages
Time Frequency Analysis Lecture Notes
This note contains below topics, Some Engineering Terminology, Notation and Recap, Basic Concepts in TimeFrequency Analysis, The ShortTime Fourier Transform, Quadratic TimeFrequency Representations, The Poisson Summation Formula, Uncertainty Principles, Gabor Systems and Frames, The Symplectic and the Metaplectic Group, Function Spaces, The Zak Transform and Density Principles, The Bargmann Transform, The Frame Set of a Window Function, A Appendices.
Author(s): Markus Faulhuber
149 Pages
Functional analysis lecture notes
This note covers normed linear spaces, Banach spaces, Linear transformations, Integration, Hilbert spaces and fourier analysis.
Author(s): T B Ward, University of East Anglia
73 Pages
Introduction to Functional Analysis by Daniel Daners
This PDF book covers the following topics related to Functional Analysis, The Axiom of Choice and Zorns Lemma, Banach Spaces, Banach algebras and the StoneWeierstrass Theorem, Hilbert Spaces, Linear Operators, Duality, Spectral Theory.
Author(s): Daniel Daners, School of Mathematics and Statistics, University of Sydney
123 Pages
Functional Analysis by Christian Remling
This note explains the following topics, Metric and topological spaces, Banach spaces, Consequences of Baires Theorem, Dual spaces and weak topologies, Hilbert spaces, Operators in Hilbert spaces, Banach algebras, Commutative Banach algebras, and Spectral Theorem.
Author(s): Christian Remling
123 Pages
This note covers the following topics, Metric and Normed Spaces, Continuous Functions, The Contraction Mapping Theorem, Topological Spaces, Banach Spaces, Hilbert Spaces, Fourier Series, Bounded Linear Operators on a Hilbert Space, The Spectrum of Bounded Linear Operators, Linear Differential Operators and Greens Functions, Distributions and the Fourier Transform, Measure Theory and Function Spaces, Differential Calculus and Variational Methods.
Author(s): John Hunter and Bruno Nachtergaele
NA Pages