Functional Analysis

Functional analysis is a branch of mathematical analysis, the core of which is formed by the study of vector spaces endowed with some kind of limit-related structure (e.g. inner product, norm, topology, etc.) and the linear functions defined on these spaces and respecting these structures in a suitable sense. The historical roots of functional analysis lie in the study of spaces of functions and the formulation of properties of transformations of functions such as the Fourier transform as transformations defining continuous, unitary etc. operators between function spaces. This point of view tu ...more

Introductory Functional Analysis with Applications
A Course in Functional Analysis
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Measure, Integration, ...
 
by
Robert B. Ash
Linear Functional Analysis
Functional Analysis
Beginning Functional Analysis
Quantum Theory for Mathematicians
Elements Of Abstract Analysis
A Course in Analysis:Vol. V: Functional Analysis, Some Operator Theory, Theory of Distributions
An Introduction to Functional Analysis
Introductory Real Analysis
Foundations of Modern Analysis
A Friendly Approach To Functional Analysis (Essential Textbooks in Mathematics)
Elements of the Theory of Functions and Functional Analysis
Applied Analysis
Functional Analysis, Sobolev Spaces and Partial Differential ... by Haïm BrézisIntroductory Functional Analysis with Applications by Erwin KreyszigElements of the Theory of Functions and Functional Analysis by A.N. KolmogorovMethods of Modern Mathematical Physics by Michael ReedAn Introduction to Banach Space Theory by Robert E. Megginson
Functional Analysis (MMath)
44 books — 6 voters

Real and Complex Analysis by Walter RudinTopology by James R. MunkresIntroductory Functional Analysis with Applications by Erwin KreyszigCounterexamples in Topology by Lynn Arthur SteenC*-Algebras and Operator Theory by Gerard J. Murphy
Mathematical Analysis
47 books — 13 voters


Paul R. Halmos
[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing—one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me. ...more
Paul R. Halmos

I am looking for partners to study Algebraic geometry, algebraic topology, commutative algebra, …more
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