Almost periodic functions. Translated from the German by Harvey Cohn. Appendixes translated by F. Steinhardt. Reprint of the 1947 English edition published by Chelsea Publishing Company. (English) Zbl 1406.42001

Dover Books on Mathematics. Mineola, NY: Dover Publications (ISBN 978-0-486-82237-2/print; 978-0-486-83328-6/ebook). 128 p. (2018).
Publisher’s description: Mathematician Harald Bohr, motivated by questions about which functions could be represented by a Dirichlet series, devised the theory of almost periodic functions during the 1920s. His groundbreaking work influenced many later mathematicians, who extended the theory in new and diverse directions. In this volume, Bohr focuses on an essential aspect of the theory – the functions of a real variable – in full detail and with complete proofs.
The treatment, which is based on Bohr’s lectures, starts with an introduction that leads to discussions of purely periodic functions and their Fourier series. The heart of the book, his exploration of the theory of almost periodic functions, is supplemented by two appendixes that cover generalizations of almost periodic functions and almost periodic functions of a complete variable.
See the revieww of German original in [Zbl 0005.20303; JFM 58.0264.01]. For the 1974 reprint of the German original see [Zbl 0278.42019].


42-02 Research exposition (monographs, survey articles) pertaining to harmonic analysis on Euclidean spaces
42A75 Classical almost periodic functions, mean periodic functions