JournalsjstVol. 4, No. 3pp. 621–642

Complex Γ\Gamma-convergence and magnetic Dirichlet Laplacian in bounded thin tubes

  • Roxana Bedoya

    Universidade Federal de São Carlos, São Carlos, Brazil
  • César R. de Oliveira

    Universidade Federal de São Carlos, São Carlos, Brazil
  • Alessandra A. Verri

    Universidade Federal de São Carlos, São Carlos, Brazil
Complex $\Gamma$-convergence and magnetic Dirichlet Laplacian in bounded thin tubes cover

Abstract

The resolvent convergence of self-adjoint operators via the technique of Γ\Gamma-convergence of quadratic forms is adapted to incorporate complex Hilbert spaces. As an application, we find effective operators to the Dirichlet Laplacian with magnetic fields in very thin bounded tubular regions in space built along smooth closed curves; the convergence is in the norm resolvent sense as the cross sections of the tubes go uniformly to zero.

Cite this article

Roxana Bedoya, César R. de Oliveira, Alessandra A. Verri, Complex Γ\Gamma-convergence and magnetic Dirichlet Laplacian in bounded thin tubes. J. Spectr. Theory 4 (2014), no. 3, pp. 621–642

DOI 10.4171/JST/81