Feng Dai
Contact
Professor, Faculty of Science - Mathematics & Statistical Sciences
- fdai@ualberta.ca
Overview
Research
Areas
Analysis
Courses
MATH 417 - Real Analysis
Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisite: MATH 317 or 414.
MATH 514 - Measure Theory I
Brief review of set operations and countable sets. Measure theory, integration theory, Lebesgue measure and integrals on R^n, product measure, Tonelli-Fubini theorem. Functions of bounded variation, absolutely continuous functions. Prerequisites: Math 317.
MATH 542 - Fourier Analysis
Review, theory and extension of Fourier series for square integrable functions; orthonormal systems, Bessel's inequality, completeness, Parseval's identity, Riesz-Fischer Theorem. Extension to Fourier series for functions in other Lebesgue classes; Fejer means, conjugate series, Dirichlet, Fejer and Poisson kernels. Norm convergence; remarks on pointwise convergence. Fourier transforms and series in several dimensions; inverse transform, Plancherel formula, Poisson Formula, maximal functions, Riesz-Thorin Theorem and applications. Elementary distribution theory; D, D', S, S' and some elementary results, Fourier transforms of tempered distributions. Examination of some earlier results with tempered distributions instead of functions and getting familiar with basic concepts. Prerequisite: MATH 418.