Spectral theory

In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operators in a variety of mathematical spaces.[1] It is a result of studies of linear algebra and the solutions of systems of linear equations and their generalizations.[2] The theory is connected to that of analytic functions because the spectral properties of an operator are related to analytic functions of the spectral parameter.[3]

  1. ^ Jean Alexandre Dieudonné (1981). History of functional analysis. Elsevier. ISBN 0-444-86148-3.
  2. ^ William Arveson (2002). "Chapter 1: spectral theory and Banach algebras". A short course on spectral theory. Springer. ISBN 0-387-95300-0.
  3. ^ Viktor Antonovich Sadovnichiĭ (1991). "Chapter 4: The geometry of Hilbert space: the spectral theory of operators". Theory of Operators. Springer. p. 181 et seq. ISBN 0-306-11028-8.