## Abstract

The basic objects in this paper are monotonically nondecreasing n x n matrix functions D(center dot) defined on some open interval l = (a, b) of R and their limit values D(a) and D(b) at the endpoints a and b which are, in general, selfadjoint relations in C-n. Certain space decompositions induced by the matrix function D(center dot) are made explicit by means of the limit values D(a) and 0(b). They are a consequence of operator inequalities involving these limit values and the notion of strictness (or definiteness) of monotonically nondecreasing matrix functions. This treatment provides a geometric approach to the square-integrability of solutions of definite canonical systems of differential equations. (C) 2011 Elsevier Inc. All rights reserved.

Original language | English |
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Pages (from-to) | 935-953 |

Number of pages | 19 |

Journal | Linear Algebra and Its Applications |

Volume | 436 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1-Mar-2012 |

## Keywords

- Monotone matrix functions
- Ordering
- Inertia
- Selfadjoint relation
- EIGENVALUE PROBLEMS
- OPERATORS
- SYSTEMS