Sumários

5 Novembro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

The Fourier transform in the Schwartz space: continuity and inverse Fourier.

Extension of the Fourier transform to L^2 (R^N): Plancherel and Parseval formulas.

The dual space of tempered distributions S'(R^N): definition and Fourier transform.

31 Outubro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Examples and exercises: the laplacian of a fundamental solution, exs. 3-4 (list 4).

29 Outubro 2019, 10:00 • Manuel Duque Pereira Monteiro Marques

The Schwartz space S(R^N) of test functions with fast decay at infinity:

definition, convergence, continuous and dense embeddings.

The Fourier transform in S(R^N).

25 Outubro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Derivative of a distribution. Higher order derivatives. The Laplacian of the Laplace's fundamental solution as a distribution.

Product of a smooth function and a distribution.

The Fourier transform in L^1(R^N): a few properties.

24 Outubro 2019, 11:00 • Manuel Duque Pereira Monteiro Marques

Higher order derivatives of distributions.

Examples and exercises (sheet 4: 1,2, part of 3).