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On the convexity of the sum of the first eigenvalues of operators depending on a real parameter

  • Miriam Bareket
Brief Reports

Abstract

Letλ1 (k)≦λ2 (k)≦⋯ be the eigenvalues of an operator of a certain type depending on a real parameterk. The paper shows that under certain requirements on the operator and on the nature of its dependence onk, the sumλ1 (k)+⋯+λ N (k) is a concave function ofk, for any positive integerN.

Keywords

Mathematical Method Real Parameter Concave Function 
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.

Zusammenfassung

Seienλ1 (k)≦2 (k)≦⋯ die Eigenwerte eines von einem reellen Parameterk abhängigen Operators. Man zeigt, daß unter gewissen Voraussetzungen über den Operator und seine Abhängigkeit vonk die Summeλ1 (k)+⋯+λN (k) für jedesN eine konkave Funktion vonk ist.

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Copyright information

© Birkhäuser Verlag 1981

Authors and Affiliations

  • Miriam Bareket
    • 1
  1. 1.Div. of Applied MathematicsTel Aviv UniversityRamat-Aviv, Tel-AvivIsrael

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