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Distribution theory Description

Key Elements

Code

MATH 403

Formation

M1 Mathematics

Semester

1

Credits

6

Number of Teaching Hours

36

Number of Tutoring Sessions

24

Number of Laboratory Sessions

0

Content

Objective

Content

• Review on the locally convex spaces and examples: C C(Ω), Ck(Ω),DK(Ω) • Definition of a distribution and preliminary properties (weak topology on the space of distributions). • Differentiation. Leibnitz Formula and Study of almost regular cases, Stokes and Green's formula and its application for finding derivations: Fundamental solution of Laplace. • Tensor Product. Fubini's Theorem and density Theorem. • Complement on topology: Banach-Steinhaus theorem and Frechet spaces (application to functional spaces). • Topology of D(Ω): the space of distributions is the topological dual of D(Ω). More properties in D’(Ω). • Convolution of distributions. • Fourier transform (L1(Ω), the space S, tempered distributions S’, L2(Ω)). • Fourier transformation of distributions. Fourier transformation and convolution: application for solving a linear PDE.