Description:
Hilbert spaces: Riesz representation theorem, Parseval's identity, Riesz-Fisher theorem, Fourier series operators. Banach spaces: Hahn-Banach theorem, open mapping and closed graph theorems, Banach-Steinhaus theorem.
Credits:
Total Credits:
Credits: 3 Lecture/Recitation/Discussion Hours:3
Description:
Hilbert spaces: Riesz representation theorem, Parseval's identity, Riesz-Fisher theorem, Fourier series operators. Banach spaces: Hahn-Banach theorem, open mapping and closed graph theorems, Banach-Steinhaus theorem.
Credits:
Total Credits:
Credits: 3 Lecture/Recitation/Discussion Hours:3
Restrictions:
Open to graduate students in the College of Natural Science or approval of department.
Description:
Hilbert spaces, Banach spaces and locally convex vector spaces. Topics include Riesz representation theorem, Parseval's identity, Riesz-Fisher theorem, Fourier series operators, Hahn-Banach theorem, open mapping and closed graph theorems, Banach-Steinhaus theorem, duality theory for locally convex spaces, convexity, Krein-Milman theorem, theory of distributions, compact operators.
Credits:
Total Credits:
Credits: 3 Lecture/Recitation/Discussion Hours:3
Restrictions:
Open to graduate students in the Applied Mathematics Major or in the Industrial Mathematics Major or in the Mathematics Major or approval of department.
Description:
Hilbert spaces, Banach spaces and locally convex vector spaces. Topics include Riesz representation theorem, Parseval's identity, Riesz-Fisher theorem, Fourier series operators, Hahn-Banach theorem, open mapping and closed graph theorems, Banach-Steinhaus theorem, duality theory for locally convex spaces, convexity, Krein-Milman theorem, theory of distributions, compact operators.