For the semiclassical Schrr odinger operator with smooth long-range potential, it is well known that the boundary values of the resolvent at non-trapping energies exist and are bounded by O(h ?1) (h being the semiclassical parameter). We present here a new proof of this result, which avoids the semiclassical Mourre theory and makes use of semiclassical measures.

We prove uniform weighted high frequency estimates for the resolvent of the Laplace-Beltrami operator on connected infinite volume Riemannian manifolds under some natural assumptions on the metric on the ends of the manifold. This extends previous results by Burq [3] and Vodev [8].

In this paper, by using a resolvent operator technique of (H,η)-monotone mappings, we study the behavior and sensitivity of the solutions for a system of variational inclusions with (H,η)-monotone operators in Hilbert spaces. Mathematics Subject Classification: 49J40, 47H19, 47H10

This work presents an alternative formulation of resolvent analysis based on the calculus variations. The proposed circumvents reliance inversion linear operator and is inherently compatible with any arbitrary choice norm. Several examples are presented which highlight analytical numerical advantages limitations formulation.

We consider second order elliptic operator with ε-periodic measurable coefficients in divergence form, acting the space ℝd. For resolvent of this we construct approximations norm $$ {\left\Vert \cdot \right\Vert}_{H^1\to {L}^2} remainder ε3 as ε → 0.

Sign type spectra are an important tool in the investigation of spectral properties of selfadjoint operators in Krein spaces. It is our aim to show that also sign type spectra for normal operators in Krein spaces provide insight in the spectral nature of the operator: If the real part and the imaginary part of a normal operator in a Krein space have real spectra only and if the growth of the re...

The publication of the important work Rauch and Taylor [RT75] started a hole branch research on wild perturbations Laplace-Beltrami operator. Here, we extend certain results show norm convergence resolvent. We consider (not necessarily compact) manifold with many small balls removed, number can increase as radius is shrinking, also be infinite. If distance shrinks less fast than radius, then th...

Abstract In this article, we focus on the scattering analysis of Sturm-Liouville type singular operator including an impulsive condition and turning point. classical literature, there are plenty papers considering positive values weight function in both continuous discontinuous cases. However, article differs from others terms appearing at We generate function, resolvent operator, discrete spec...