It is by no means easy for the applied mathematician to decide how much importance he should attach to the more abstract and aesthetic side of his work ... To all appearances, Sir William Rowan Hamilton (1850-1865) attached little importance to the practical applications of his method, and it was only with the publication of his Mathematical Papers that it was possible to form a more correct and balanced judgement of Hamilton as an applied mathematician.

This tract gives a clear exposition of the elementary theory of Fourier transforms, so arranged as to give easy access to the recently developed abstract theory of Fourier transforms on a locally compact group. (This latter subject has important applications to the general treatment of unitary representations of the rotation group, the Lorentz group and other classical groups that is of value in quantum field theory and other branches of mathematical physics.) A knowledge of Lebesgue integration and, in one chapter, of Riemann-Stieltjes integration is assumed; the results needed are all stated in the introductory chapter.

"The Barth-Harnack exchange is remarkably relevant to contemporary contestations of the proper method of Christian theology and its relation to the historical and social-scientific study of religion. The reissue of this translation, together with the expert analysis and assessment of H. Martin Rumscheidt, is a welcome event." --David Fergusson, Professor of Divinity and Principal of New College, University of Edinburgh

This 1996 book is a comprehensive account of the theory of Lévy processes; aimed at probability theorists.

An introduction to the modern theory of ideas.

Professor Rogers has written this economical and logical exposition of the theory of packing and covering at a time when the simplest general results are known and future progress seems likely to depend on detailed and complicated technical developments. The book treats mainly problems in n-dimensional space, where n is larger than 3. The approach is quantative and many estimates for packing and covering densities are obtained. The introduction gives a historical outline of the subject, stating results without proof, and the succeeding chapters contain a systematic account of the general results and their derivation. Some of the results have immediate applications in the theory of numbers, in analysis and in other branches of mathematics, while the quantative approach may well prove to be of increasing importance for further developments.

Originally published in 1934, this volume presents the theory of the distribution of the prime numbers in the series of natural numbers. Despite being long out of print, it remains unsurpassed as an introduction to the field.