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This book gives a thorough introduction on classical Fourier transforms in a compact and self-contained form. Chapter I is devoted to the L1-theory: basic properties are proved as well as the Poisson summation formula, the central limit theorem and Wiener`s general tauberian theorem. As an illustraiton of a Fourier transformation of a function not belonging to L1 (- , ) an integral due to Ramanujan is given. Chapter II is devoted to the L2-theory, including Plancherel`s theorem, Heisenberg`s inequality, the Paley-Wiener theorem, Hardy`s interpolation formula and two inequalities due to Bernstein. Chapter III deals with Fourier-Stieltjes transforms. After the basic properties are explained, distribution functions, positive-definite functions and the uniqueness theorem of Offord are treated. The book is intended for undergraduate students and requires of them basic knowledge in real and complex analysis.ISBN - 9783540502487
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Pages : 172
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