10 citations · 53 across the 16 of their papers we have counts for
16 papers
Discrete approximations to Dirichlet and Neumann Laplacians on a half-space and norm resolvent convergence
Horia Cornean, Henrik Garde, Arne Jensen
We extend recent results on discrete approximations of the Laplacian in with norm resolvent convergence to the corresponding results for Dirichlet and Neumann Laplac…
Discrete approximations to Dirac operators and norm resolvent convergence
Horia D. Cornean, Henrik Garde, Arne Jensen
We consider continuous Dirac operators defined on , , together with various discrete versions of them. Both forward-backward and symmetric finite diffe…
Norm resolvent convergence of discretized Fourier multipliers
Horia Cornean, Henrik Garde, Arne Jensen
We prove norm estimates for the difference of resolvents of operators and their discrete counterparts, embedded into the continuum using biorthogonal Riesz sequences. The estimates…
Continuum limit for lattice Schrödinger operators
Hiroshi Isozaki, Arne Jensen
We study the behavior of solutions of the Helmholtz equation on a periodic lattice as the mesh size tends to 0. Projecting to the eigenspace of a…
Hypergeometric expression for the resolvent of the discrete Laplacian in low dimensions
Kenichi Ito, Arne Jensen
We present an explicit formula for the resolvent of the discrete Laplacian on the square lattice, and compute its asymptotic expansions around thresholds in low dimensions. As a by…
A solvable model of the breakdown of the adiabatic approximation
Artbazar Galtbayar, Arne Jensen, Kenji Yajima
Let and . Consider the following time-dependent family of Schrödinger equations with scaled and translated harmonic oscillator potentials $ i\varep…