Eigenvalues of Positive Definite Integral Operators on Unbounded Intervals

  title={Eigenvalues of Positive Definite Integral Operators on Unbounded Intervals},
  author={J. Buescu and A. Paix{\~a}o},
  • J. Buescu, A. Paixão
  • Published 2006
  • Mathematics
  • Positivity
  • Let k(x, y) be the positive definite kernel of an integral operator on an unbounded interval of ℝ. If k belongs to class defined below, the corresponding operator is compact and trace class. We establish two results relating smoothness of k and its decay rate at infinity along the diagonal with the decay rate of the eigenvalues. The first result deals with the Lipschitz case; the second deals with the uniformly C1 case. The optimal results known for compact intervals are recovered as special… CONTINUE READING
    8 Citations


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