Basic Information
The Stone-weierstrass Theorem. Hilbert Spaces, Convex Sets And Projections, Orthonormal Systems, The Riesz Representation Theorem And Its Applications. Fourier Series# Convergence in Norm, Uniform Convergence, Convergence Theorems of Fejer and Dirichlet. Normed Spaces, Banach Spaces, The Algebra of Bounded Operators, The Dual Space, Compact Operators, Fredholm S Alternative. The Spectral Theorem For Compact Selfadjoint Operators On a Hilbert Space and Its Applications. The Maximum-minimum Theorem, The Functional Calculus For Compact Normal Operators. Fourier Tranforms# The Fourier Tranform On L1 and On L2, Applications of The Fourier Transform. The Laplace Transform, Applications of The Laplace Transform.
Faculty: Mathematics
|Undergraduate Studies
Pre-required courses
(104142 - Int. to Metric and Topological Space and 104168 - Algebra B and 104281 - Infinitesimal Calculus 2)
Parallel course
104122 - Complex Function Theory 1
Course with no extra credit
104221 - Complex Functions and Integral Transform 104223 - Partial Differen.equa.and Fourier Series
Course with no extra credit (contained)
104214 - Fourier Series and Integral Transforms 104276 - Introduction to Functional Analysis