Limit properties of monotone matrix functions

Jussi Behrndt, Seppo Hassi, Henk de Snoo*, Rudi Wietsma

*Corresponding author for this work

    Research output: Contribution to journalArticleAcademicpeer-review

    3 Citations (Scopus)
    16 Downloads (Pure)

    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 languageEnglish
    Pages (from-to)935-953
    Number of pages19
    JournalLinear Algebra and Its Applications
    Volume436
    Issue number5
    DOIs
    Publication statusPublished - 1-Mar-2012

    Keywords

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

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