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.
Fixed point theory in fuzzy metric spaces has grown to become an intensive field of research. However, due to the complexity involved in the nature of fuzzy metrics, the authors need to develop innovative machinery to establish new fixed point theorems in such kind of spaces. In this paper, we propose the concepts of asymptotic fuzzy -contractive and asymptotic fuzzy Meir-Keeler mappings, and describe some new machinery by which the corresponding fixed point theorems are proved. In this sense,...
A new criterion of asymptotic periodicity of Markov operators on , established in [3], is extended to the class of Markov operators on signed measures.
New sufficient conditions for asymptotic stability of Markov operators are given. These criteria are applied to a class of Volterra type integral operators with advanced argument.
We study the asymptotic behavior of the solutions of a differential equation with unbounded delay. The results presented are based on the first Lyapunov method, which is often used to construct solutions of ordinary differential equations in the form of power series. This technique cannot be applied to delayed equations and hence we express the solution as an asymptotic expansion. The existence of a solution is proved by the retract method.
Let G be a finite connected graph on two or more vertices, and the distance-k graph of the N-fold Cartesian power of G. For a fixed k ≥ 1, we obtain explicitly the large N limit of the spectral distribution (the eigenvalue distribution of the adjacency matrix) of . The limit distribution is described in terms of the Hermite polynomials. The proof is based on asymptotic combinatorics along with quantum probability theory.
A new theorem on asymptotic stability and sweeping of substochastic semigroups is proved, and applied semigroups generated by birth-death processes.
Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by , where is a finite-valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a necessary asymptotic stability condition.
We study the asymptotic behaviour of solutions of a transport equation. We give some sufficient conditions for the complete mixing property of the Markov semigroup generated by this equation.