ABSTRACT
A function space is the general name for essentially any set of functions satisfying some particular criteria, which may differ between different function spaces. Linear operators on different vector spaces in general, and on function spaces in particular, will appear in a large variety of different physical situations. Separation of variables is a technique that may be used to find solutions to some differential equations. The function space in question is the space of functions with finite norm under this inner product. The example shows that the eigen functions of periodic Sturm—Liouville problems are not necessarily non-degenerate. It may also happen that the interval is not finite, but that we are studying functions on an infinite interval. In this case, the requirement on the function space is that the functions should have finite norms according to the inner product.
