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Factorization of matrix functions analytic in a strip

  • Harm Bart
  • Marinus A. Kaashoek
  • André C. M. Ran
Part of the Operator Theory: Advances and Applications book series (OT, volume 200)

Abstract

This chapter deals with m × m matrix-valued functions of the form
$$ W(\lambda ) = I - \int_{ - \infty }^\infty {e^{i\lambda t} k(t)dt,} $$
(5.1)
where k is an m × m matrix-valued function with the property that for some ω < 0 the entries of e−ω|t|k(t) are Lebesgue integrable on the real line. In other words, k is of the form
$$ k(t) = e^{\omega |t|} h(t) with h \in L_1^{m \times m} (\mathbb{R}). $$
(5.2)
It follows that the function W is analytic in the strip \( \left| {\mathfrak{F}\lambda } \right| \), where τ=−ω. This strip contains the real line. The aim is to extend the canonical factorization theorem of Chapter 5 to functions of the type (5.1).

Keywords

Kernel Function Real Line Matrix Function Bounded Linear Operator Exponential Type 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser/Springer Basel AG 2010

Authors and Affiliations

  • Harm Bart
    • 1
  • Marinus A. Kaashoek
    • 2
  • André C. M. Ran
    • 2
  1. 1.Econometrisch InstituutErasumus Universiteit RotterdamRotterdamThe Netherlands
  2. 2.Department of Mathematics, FEWVrije UniversiteitAmsterdamThe Netherlands

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