Komaravolu Chandrasekharan

Classical Fourier Transforms (eBook, PDF)

• Format: PDF

Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 172
• Erscheinungstermin: 6. Dezember 2012
• Englisch
• ISBN-13: 9783642740299
• Artikelnr.: 53384023

Inhaltsangabe

I. Fourier transforms on L1 (-?,?).-
1. Basic properties and examples.-
2. The L1 -algebra.-
3. Differentiability properties.-
4. Localization, Mellin transforms.-
5. Fourier series and Poisson's summation formula.-
6. The uniqueness theorem.-
7. Pointwise summability.-
8. The inversion formula.-
9. Summability in the L1-norm.-
10. The central limit theorem.-
11. Analytic functions of Fourier transforms.-
12. The closure of translations.-
13. A general tauberian theorem.-
14. Two differential equations.-
15. Several variables.- II. Fourier transforms on L2(-?,?).-
1. Introduction.-
2. Plancherel's theorem.-
3. Convergence and summability.-
4. The closure of translations.- 5. Heisenberg's inequality.-
6. Hardy's theorem.-
7. The theorem of Paley and Wiener.-
8. Fourier series in L2(a,b).-
9. Hardy's interpolation formula.-
10. Two inequalities of S. Bernstein.-
11. Several variables.- III. Fourier-Stieltjes transforms (one variable).-
1. Basic properties.-
2. Distribution functions, and characteristic functions.-
3. Positive-definite functions.-
4. A uniqueness theorem.- Notes.- References.Summary of the Contents:
Fourier transforms on L1-theory.- Fourier transforms on L2-theory.- Fourier-Stieltjes transforms (one variable).- Notes.- References.