Annali di Matematica Pura ed Applicata

, Volume 188, Issue 1, pp 123–151 | Cite as

An algebraic foundation for factoring linear boundary problems

Article

Abstract

Motivated by boundary problems for linear differential equations, we define an abstract boundary problem as a pair consisting of a surjective linear map (“differential operator”) and an orthogonally closed subspace of the dual space (“boundary conditions”). Defining the composition of boundary problems corresponding to their Green’s operators in reverse order, we characterize and construct all factorizations of a boundary problem from a given factorization of the defining operator. For the case of ordinary differential equations, the main results can be made algorithmic. We conclude with a factorization of a boundary problem for the wave equation.

Keywords

Linear boundary value problems Factorization Green’s operators 

Mathematics Subject Classification (2000)

47A68 34B05 35G15 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  1. 1.Johann Radon Institute for Computational and Applied Mathematics (RICAM)Austrian Academy of SciencesLinzAustria

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