This monograph provides a comprehensive treatment of expansion
theorems for regular systems of first order differential equations
and "n"-th order ordinary differential equations.
In 10 chapters and one appendix, it provides a comprehensive
treatment from abstract foundations to applications in physics and
engineering. The focus is on non-self-adjoint problems. Bounded
operators are associated to these problems, and Chapter 1 provides
an in depth investigation of eigenfunctions and associated
functions for bounded Fredholm valued operators in Banach spaces.
Since every "n"-th order differential equation is equivalent
to a first order system, the main techniques are developed for
systems. Asymptotic fundamental
systems are derived for a large class of systems of differential
equations. Together with boundary
conditions, which may depend polynomially on the eigenvalue
parameter, this leads to the definition of Birkhoff and Stone
regular eigenvalue problems. An effort is made to make the
conditions relatively easy verifiable; this is illustrated with
several applications in chapter 10.
The contour integral method and estimates of the resolvent are used
to prove expansion theorems.
For Stone regular problems, not all functions are expandable, and
again relatively easy verifiable
conditions are given, in terms of auxiliary boundary conditions,
for functions to be expandable.
Chapter 10 deals exclusively with applications; in nine sections,
various concrete problems such as
the Orr-Sommerfeld equation, control of multiple beams, and an
example from meteorology are investigated.
Key features:
Expansion Theorems for Ordinary Differential Equations
Discusses Applications to Problems from Physics and
Engineering
Thorough Investigation of Asymptotic Fundamental Matrices and
Systems
Provides a Comprehensive Treatment
Uses the Contour Integral Method
Represents the Problems as Bounded Operators
Investigates Canonical Systems of Eigen- and Associated Vectors
for Operator Functions
"
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