Is there some sufficient condition on the kernel $K$ of a (say, finite rank, to simplify) integral operator $$ \mathcal K:f(x)\in L^2(\mathbb R)\mapsto \int K(x,y)f(y)dy $$ so that it has all its non-zero eigenvalues $\textbf{distinct}$ (i.e. with multiplicity one) ?

  • 6
    $\begingroup$ I can refer you to this paper. $\endgroup$ Commented Aug 25, 2012 at 12:34
  • 5
    $\begingroup$ A finite-rank operator on an infinite-dimensional Banach space has infinite-dimensional kernel. Are you talking about the nonzero eigenvalues? $\endgroup$ Commented Aug 25, 2012 at 23:17


You must log in to answer this question.