In this article, we deeply reveal the relationship between functions and in an overlap function additively generated by an additive generator pair (,), which is used to characterize the conditions for an overlap function additively generated by the pair being a triangular norm by terms of functions and . We also establish the conditions that an overlap function additively generated by the additive generator pair can be obtained by a distortion of a triangular norm and a (pseudo) automorphism....
In this article, we give a necessary and sufficient condition in the perturbation regime on the existence of eigenvalues embedded between two thresholds. For an eigenvalue of the unperturbed operator embedded at a threshold, we prove that it can produce both discrete eigenvalues and resonances. The locations of the eigenvalues and resonances are given.
We correct an error in the normalizing constant of resonant states.
For Schrödinger operator on Riemannian manifolds with conical end, we study the contribution of zero energy resonant states to the singularity of the resolvent of near zero. Long-time expansion of the Schrödinger group is obtained under a non-trapping condition at high energies.
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