Difference between revisions of "Functional Analysis"

Revision as of 14:19, 8 May 2008

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

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+== Chris Grant's Proposed Core Topics List for a 500-level Linear Course==
+<div style="-moz-column-count:2; column-count:2;">
+#  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
+</div>
 == Courses ==
 * [[Math 645]]:  Functional Analysis (1?)
 * [[Math 646]]:  Functional Analysis (2?)