Fourier series

See Fourier series for more information, including the historical development.

He is best known for starting the investigation of Fourier series.

This class of functions can be expanded in Fourier series.

This fact is a central one in Fourier series.

It is called a Fourier series if the terms and have the form:

The same condition also occurs in the uniqueness problem for Fourier series.

This is fundamental to the study of Fourier series.

A complex-number form of Fourier series is also commonly used.

The distorted signal can be described by a Fourier series in f.

Hardy spaces in the disc are related to Fourier series.

We now use the formula above to give a Fourier series expansion of a very simple function.

This superposition or linear combination is called the Fourier series.

Since Fourier series have such good convergence properties, many are often surprised by some of the negative results.

I will have all machines capable of handling Fourier series and up cleared for your use.

There is an intimate connection between power series and Fourier series.

This particular Fourier series is troublesome because of its poor convergence properties.

In his free time he worked on Fourier series, a topic which interested him throughout his life.

In mathematical analysis, many generalizations of Fourier series have proved to be useful.

One can ask if there is in some sense a largest natural space of functions whose Fourier series converge almost everywhere.

The Fourier series of a periodic even function includes only cosine terms.

If that is the property which we seek to preserve, one can produce Fourier series on any compact group.

The question of determining when a Fourier series converges has been fundamental for centuries.

Expansion in a Fourier series will provide an equation of motion to arbitrary precision.

Here we presume an understanding of basic multivariate calculus and Fourier series.

Fourier series are also applicable to subjects whose connection with wave motion is far from obvious.