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Integration II Description

Key Elements

Code

MATH 306

Formation

BS Mathematics

Semester

6

Credits

6

Number of Teaching Hours

30

Number of Tutoring Sessions

30

Number of Laboratory Sessions

0

Content

Objective

1. Know Fubini theorem, use it to determine some integrales "doubles and triples". 2. Lebesgue measure in Rⁿ. 3. Determine a function that we know its Fourier transform. 4. Compute the convolution product. 5. Know the relations between the convergence in Lp and the simple convergence(construction of a sequence ). 6. Apply the Hilbert technique in L2. 7. Technique of density of a measure. Function absolutely continuous. 8. Duality injection and compacity between the spaces in Lp or the construction of a measure et the Theorem of Daniel.

Content

 Measures products, Measure of Lebesgue in Rⁿ. Theorems of Tonelli and Fubini. Convolution in L1, properties of the Fourier transform in L1.  Analytical study of the spaces L2,orthogonal system et orthonormal. Inversion of the Fourier transform in L1 and L2, Fourier-Plancherel, L2(T).  Space Lp, Theorem of Radon – Nykodim, measure absolutely continuous, singular measure.  Duality injection and compacity between the spaces Lp or the construction of a measure and the Theorem of Daniel.