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

  • Miriam Bareket
Brief Reports


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.


Mathematical Method Real Parameter Concave Function 
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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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