Difference between revisions of "Functional Analysis"
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| − | == Chris Grant's Proposed Core Topics List for | + | == Courses == |
| + | * [[Math 540]]: Linear Analysis | ||
| + | * [[Math 640]]: Nonlinear Analysis | ||
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| + | == Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses == | ||
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| + | === Function Spaces === | ||
<div style="-moz-column-count:2; column-count:2;"> | <div style="-moz-column-count:2; column-count:2;"> | ||
# Distribution theory | # Distribution theory | ||
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#* Schwartz class and tempered distributions | #* Schwartz class and tempered distributions | ||
#* Operations on 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 |
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</div> | </div> | ||
| − | == | + | === Semigroups === |
| − | + | # Hille-Yosida theorem | |
| − | + | # Lumer-Phillips theorem | |
| + | # Friedrich's lemma | ||
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| + | [[Category:Areas]] | ||
Latest revision as of 12:17, 4 June 2009
Contents
Courses
Chris Grant's Proposed Core Topics List for Some Functional Analysis Courses
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
