Spectral Theory of Block Operator Matrices

Project: Research

Description

Block operator matrices are matrices whose entries are operators in Hilbert or Banach spaces. Such operators appear in a natural way when systems of differential equations with different order and type are investigated or an operator in a given space is considered that has a natural decomposition intosubspaces. In many applications of mathematical physics it is natural and fruitful to use the theory of block operator matrices. It is the aim to study spectral properties of such block operator matrices: location of the essential spectrum, variational principles and estimates for eigenvalues, investigation of spectral subspaces, basis properties of components of eigenvectors and generalised Fourier transforms. Particular emphasis is placed on unbounded block operator matrices, for which different cases have to be considered separately; these cases depend on the places where the strongest operators are located. The results should be applied to concrete operators arising in applications, mainly ordinary or partial differential operators.
StatusFinished
Effective start/end date1/09/0730/11/09

Funding

  • EPSRC (Engineering and Physical Sciences Research Council): £188,958.00

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Operator Matrix
Block Matrix
Spectral Theory
Operator
Generalized Fourier Transform
Partial Differential Operators
Essential Spectrum
System of Differential Equations
Spectral Properties
Variational Principle
Eigenvector
Hilbert space
Subspace
Physics
Banach space
Eigenvalue
Decompose
Estimate