Classical Fourier Transforms

Front Cover
Springer Berlin Heidelberg, Dec 22, 1988 - Mathematics - 172 pages
In gratefuZ remerribrance of Marston Morse and John von Neumann This text formed the basis of an optional course of lectures I gave in German at the Swiss Federal Institute of Technology (ETH), Zlirich, during the Wintersemester of 1986-87, to undergraduates whose interests were rather mixed, and who were supposed, in general, to be acquainted with only the rudiments of real and complex analysis. The choice of material and the treatment were linked to that supposition. The idea of publishing this originated with Dr. Joachim Heinze of Springer­ Verlag. I have, in response, checked the text once more, and added some notes and references. My warm thanks go to Professor Raghavan Narasimhan and to Dr. Albert Stadler, for their helpful and careful scrutiny of the manuscript, which resulted in the removal of some obscurities, and to Springer-Verlag for their courtesy and cooperation. I have to thank Dr. Stadler also for his assistance with the diagrams and with the proof-reading. Zlirich, September, 1987 K. C. Contents Chapter I. Fourier transforms on L (-oo,oo) 1 §1. Basic properties and examples •. •••••. . ••. . •. •. . . •. •. . •. . . . • 1 §2. The L 1-algebra ••. . . . . . . ••••. . ••. •. . ••. . ••. . •. . . ••. . . . ••. •. . 16 §3. Differentiabili ty properties . . . •••. •. •••••••. . . . ••••. •. . . •. 18 §4. Localization, Mellin transforms . . . . . . •. •. . . . . . •. . . . . . •. . •. . 25 §5. Fourier series and Poisson's summation formula . . . . . . . ••. ••. . 32 §6. The uniqueness theorem . . . . . . . •. . . . . . . . . . . •. . . . •. . . . . . . . . . . .

From inside the book

What people are saying - Write a review

We haven't found any reviews in the usual places.

Contents

Fourier transforms on In 0000
1
2 The L1algebra
2
3 Differentiability properties
18
Copyright

29 other sections not shown

Other editions - View all

Common terms and phrases

Bibliographic information