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On a Rational Function in a Linear Relation

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Abstract

The behavior of the domain, the range, the kernel and the multi-valued part of a rational function in a linear relation is analyzed, respectively. We give some basic properties of such linear relations, and we prove that the rational form of the spectral mapping theorem holds in terms of ascent, essential ascent, descent and essential descent.

Keywords

Linear relation Ascent Descent Spectral mapping theorem Rational function 

Mathematics Subject Classification

47A06 47A53 47A10 

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Copyright information

© Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia 2018

Authors and Affiliations

  1. 1.Department of MathematicsPrince Sattam bin Abdulaziz UniversityAl kharjSaudi Arabia
  2. 2.Department of Mathematics, Faculty of sciences of SfaxUniversity of SfaxSfaxTunisia

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