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Fourier Analysis - Theory and Applications >> Content Detail



Lecture Notes



Lecture Notes

The lecture notes are courtesy of Jonathan Campbell, a student in the class. Notes for the entire course are available as a single pdf file (PDF) (Courtesy of Jonathan A. Campbell. Used with permission.), or broken into files corresponding to the lectures. 

LEC #TOPICS
1Introduction (PDF)
2Measures (PDF)
3Chebyshev's Inequality (PDF)
4Law of Large Numbers (PDF)
5Measurable Functions (PDF)
6The Integral (PDF)
7Linearity (PDF)
8Fatou's Lemma (PDF)
9Integrable Functions (PDF)
10Bessel's Inequality (PDF)
11Convergence of Fourier Series (PDF)
12Completeness (PDF)
13First In-class Test
14Riesz Representation Theorem (PDF)
15Schwartz Functions (PDF)
16Fourier Transform (PDF)
17Approximation (PDF)
18Harmonic Oscillator (PDF)
19Completeness of Eigenfunctions (PDF)
20Sobolev Spaces (PDF)
21Second In-class Test
22Wave Equation (PDF)
23Bounded Operators (PDF)
24Compact Operators (PDF)
25Spectral Theorem (PDF)
26Hilbert-Schmidt Operators (PDF)
27Final Exam




 








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