To send content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about sending content to .
To send content items to your Kindle, first ensure firstname.lastname@example.org
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about sending to your Kindle.
Note you can select to send to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be sent to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
The first edition of this book was written almost twenty-five years ago. Since then the theory of trigonometric series has undergone considerable change. It has always been one of the central parts of Analysis, but now we see its notions and methods appearing, in abstract form, in distant fields like the theory of groups, algebra, theory of numbers. These abstract extensions are, however, not considered here and the subject of the second edition of this book is, as before, the classical theory of Fourier series, which may be described as the meeting ground of the Real and Complex Variables.
This theory has been a source of new ideas for analysts during the last two centuries, and is likely to be so in years to come. Many basic notions and results of the theory of functions have been obtained by mathematicians while working on trigonometric series. Conceivably these discoveries might have been made in different contexts, but in fact they came to life in connexion with the theory of trigonometric series. It was not accidental that the notion of function generally accepted now was first formulated in the celebrated memoir of Dirichlet (1837) dealing with the convergence of Fourier series; or that the definition of Riemann's integral in its general form appeared in Riemann's Habilitationsschrift devoted to trigonometric series; or that the theory of sets, one of the most important developments of nineteenth-century mathematics, was created by Cantor in his attempts to solve the problem of the sets of uniqueness for trigonometric series.