Classical Fourier Transforms [Paperback]

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 Poissons 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. Plancherels theorem.- ?3. Convergence and summability.- ?4. The closure of translations.- ?5. Heisenbergs inequality.- ?6. Hardys theorem.- ?7. The theorem of Paley and Wiener.- ?8. Fourier series in L2(a,b).- ?9. Hardys 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.Springer Book ArchivesDE