Sumários
Lecture 14: Fourier Transform, part III. Sobolev Spaces, part I
9 Abril 2019, 10:30 • Hugo Tavares
The derivative of a temperate distribution is a temperate distribution. A polynomial times a tempered distribution is a tempered distribution. Formulas for derivatives of tempered distributions.
Introduction to the Sobolev Spaces W^{k,p}(Omega): definition, norms, examples, elementary properties.
Lecture 13. Fourier Transform, part II
5 Abril 2019, 12:00 • Hugo Tavares
The Schwarz space: embeddings and dense sets.
Extension to L^2: Plancherel's and Parseval's formulas.
Lecture 12: Distributions part II; Fourier Transform part I
2 Abril 2019, 10:30 • Hugo Tavares
Higher order derivative of a distribution. COmputation of the derivative of the fundamental solution of the Laplace Equation in the sense of distributions.
Definition of Fourier Transform and Inverse Fourier Transform in L^1.
The Schwarz space, definition of convergence.
Lecture 11: Distributions, part I
29 Março 2019, 12:00 • Hugo Tavares
The theory of distributions.
- Definition of the test function space, and notion of convergence