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.
Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828
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.
Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828
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.
Semester:
Spring of every year
Credits:
Total Credits: 3 Lecture/Recitation/Discussion Hours: 3
Recommended Background:
MTH 828
Restrictions:
Open to graduate students or master's students or doctoral 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.