Difference between revisions of "Functional Analysis"
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== Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses == | == Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses == | ||
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=== Nonlinear Analysis === | === Nonlinear Analysis === | ||
<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
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=== Function Spaces === | === Function Spaces === | ||
<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
| + | # Distribution theory | ||
| + | #* Test functions and distributions | ||
| + | #* Schwartz class and tempered distributions | ||
| + | #* Operations on distributions | ||
# Imbedding theorems | # Imbedding theorems | ||
# Compact imbeddings | # Compact imbeddings | ||
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== Courses == | == Courses == | ||
| + | * [[Proposed Linear Analysis Course]] | ||
* [[Math 645]]: Functional Analysis (1?) | * [[Math 645]]: Functional Analysis (1?) | ||
* [[Math 646]]: Functional Analysis (2?) | * [[Math 646]]: Functional Analysis (2?) | ||
[[Category:Areas]] | [[Category:Areas]] | ||
Revision as of 10:19, 3 June 2008
Contents
Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses
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
- Distribution theory
- Test functions and distributions
- Schwartz class and tempered distributions
- Operations on distributions
- 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
Courses
- Proposed Linear Analysis Course
- Math 645: Functional Analysis (1?)
- Math 646: Functional Analysis (2?)
