Linear Mathematics In Infinite Dimensions: Signals, Boundary Value Problems and Special Functions

The main focus of the book is on the mathematical framework that underlies linear systems arising in physics, engineering and applied mathematics. Roughly speaking, we are making a generalization from the theory of linear transformation on finite dimensional vector space to the theory of linear operators on infinite dimensional vector spaces as they occur in the context of homogeneous and inhomogeneous boundary value and initial value problems.

All key ideas of linear mathematics in infinite dimensions are already present with waves, signals, and fields whose domains are one-dimensional. The transition to higher dimensional domains is very smooth once these ideas have been digested. This transition does, however, have a few pleasant surprises.