Eigenvalues of the Truncated Helmholtz Solution Operator under Strong Trapping

Asymptotic distribution of eigenvalues of the elliptic operator system

Since the theory of spectral properties of non-self-accession differential operators on Sobolev spaces is an important field in mathematics, therefore, different techniques are used to study them. In this paper, two types of non-self-accession differential operators on Sobolev spaces are considered and their spectral properties are investigated with two different and new techniques.

Strong Convergence Rates of the Product-limit Estimator for Left Truncated and Right Censored Data under Association

Non-parametric estimation of a survival function from left truncated data subject to right censoring has been extensively studied in the literature. It is commonly assumed in such studies that the lifetime variables are a sample of independent and identically distributed random variables from the target population. This assumption is often prone to failure in practical studies. For instance, wh...

Asymptotics of Eigenvalues of the Schrr Odinger Operator with a Strong -interaction on a Loop

In this paper we investigate the operator H = ??(??) in L 2 (R 2), where > 0 and ? is a closed C 4 Jordan curve in R 2. We obtain the asymptotic form of each eigenvalue of H as tends to innnity. We also get the asymptotic form of the number of negative eigenvalues of H in the strong coupling asymptotic regime.

Asymptotics of eigenvalues of the Schrödinger operator with a strong δ-interaction on a loop

In this paper we investigate the operator Hβ = −∆−βδ(·−Γ) in L (R), where β > 0 and Γ is a closed C Jordan curve in R. We obtain the asymptotic form of each eigenvalue of Hβ as β tends to infinity. We also get the asymptotic form of the number of negative eigenvalues of Hβ in the strong coupling asymptotic regime. MSC: 35J10, 35P15

Vekua theory for the Helmholtz operator