39 citations · 66 across the 9 of their papers we have counts for
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Influence of the bound states in the Neumann Laplacian in a thin waveguide
Carlos R. Mamani, Alessandra A. Verri
We study the Neumann Laplacian operator restricted to a twisted waveguide . The goal is to find the effective operator when the diameter of tends to zero. However,…
A note on the spectrum of the Neumann Laplacian in periodic waveguides
Alessandra A. Verri, Carlos R. Mamani
We study the Neumann Laplacian restricted to a periodic waveguide. In this situation its spectrum presents a band structure. Our goal and strategy is to get spectr…
Absolute continuity and band gaps of the spectrum of the Dirichlet Laplacian in periodic waveguides
Carlos R. Mamani, Alessandra A. Verri
Consider the Dirichlet Laplacian operator in a periodic waveguide . On the condition that is sufficiently thin, we show that its spectrum is absolutely cont…
Complex -convergence and magnetic Dirichlet Laplacian in bounded thin tubes
R. Bedoya, C. R. de Oliveira, A. A. Verri
The resolvent convergence of self-adjoint operators via the technique of -convergence of quadratic forms is adapted to incorporate complex Hilbert spaces. As an application, we…
Mathematical predominance of Dirichlet condition for the one-dimensional Coulomb potential
Cesar R. de Oliveira, Alessandra A. Verri
We restrict a quantum particle under a coulombian potential (i.e., the Schrödinger operator with inverse of the distance potential) to three dimensional tubes along the x-axis and…
On the spectrum and weakly effective operator for Dirichlet Laplacian in thin deformed tubes
Cesar R. de Oliveira, Alessandra A. Verri
We study the Laplacian in deformed thin (bounded or unbounded) tubes in ?, i.e., tubular regions along a curve whose cross sections are multiplied by an appropriate de…