Difference between revisions of "Functional Analysis"
From MathWiki
Line 73: | Line 73: | ||
* [[Math 645]]: Functional Analysis (1?) | * [[Math 645]]: Functional Analysis (1?) | ||
* [[Math 646]]: Functional Analysis (2?) | * [[Math 646]]: Functional Analysis (2?) | ||
+ | |||
+ | [[Category:Areas]] |
Revision as of 13:17, 19 May 2008
Contents
Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses
Linear Analysis
- Distribution theory
- Test functions and distributions
- Schwartz class and tempered distributions
- Operations on distributions
- Hilbert spaces
- Riesz representation theorem
- Projection theorem
- Lax-Milgram theorem
- Existence of an orthonormal basis
- Fredholm alternative
- Hahn-Banach theorem
- Banach spaces
- Banach-Steinhaus theorem
- Alaoglu’s theorem
- Open mapping theorem
- Bounded inverse theorem
- Closed graph theorem
- Baire category theorem
- Normed linear spaces
- Spectral radius of bounded operators
- Riesz-Schauder theorem
- Analyticity of resolvent operator
- Nonemptiness of spectrum
- Adjoints of bounded/unbounded operators
- Hilbert-Schmidt theorem
Nonlinear Analysis
- Variational problems
- Euler-Lagrange equations
- Abstract Dirichlet principle
- Mazur’s lemma
- Tonelli’s theorem
- Mountain pass theorem
- Fixed-point problems
- Contraction mapping principle
- Inverse function theorem
- Implicit function theorem
- Brouwer fixed-point theorem
- Schauder fixed-point theorem
- Schaefer’s fixed-point theorem
- Leray-Schauder fixed-point theorem
- Browder-Minty fixed-point theorem
Function Spaces
- Imbedding theorems
- Compact imbeddings
- Poincaré inequalities
- Rellich-Kondrachov theorem
- Morrey's theorem
- Caccioppoli inequality
- John-Nirenberg inequality
- Calderón-Zygmund inequality
- Trace theorem
- Marcinkiewicz interpolation theorem
Semigroups
- Hille-Yosida theorem
- Lumer-Phillips theorem
- Friedrich's lemma