TY - JOUR
T1 - Exponential estimates of solutions of pseudodifferential equations on the lattice h ℤn
T2 - Applications to the lattice Schrödinger and Dirac operators
AU - Rabinovich, V.
N1 - Funding Information:
The work was supported by the CONACYT project 81615, Mexico.
PY - 2010
Y1 - 2010
N2 - The main aim of the paper is the application of the calculus of pseudodifferential operators on the lattice ℤn ={x ∈ ℝn:x=hy,y ∈ ℤndepending on a small parameter h > 0 to exponential estimates of solutions of difference equations on (hℤ)n. As an application of general results we obtain the local exponential decreasing of eigenfunctions of Schrödinger and Dirac operators on the lattice h→ 0 for h → 0. These results can be considered as an analog of the well known tunnel effect for Schrödinger operators on ℝn.
AB - The main aim of the paper is the application of the calculus of pseudodifferential operators on the lattice ℤn ={x ∈ ℝn:x=hy,y ∈ ℤndepending on a small parameter h > 0 to exponential estimates of solutions of difference equations on (hℤ)n. As an application of general results we obtain the local exponential decreasing of eigenfunctions of Schrödinger and Dirac operators on the lattice h→ 0 for h → 0. These results can be considered as an analog of the well known tunnel effect for Schrödinger operators on ℝn.
KW - Lattice Schrödinger and Dirac operators
KW - Pseudodifferential operators on the lattice
UR - http://www.scopus.com/inward/record.url?scp=84873060717&partnerID=8YFLogxK
U2 - 10.1007/s11868-010-0005-2
DO - 10.1007/s11868-010-0005-2
M3 - Artículo
SN - 1662-9981
VL - 1
SP - 233
EP - 253
JO - Journal of Pseudo-Differential Operators and Applications
JF - Journal of Pseudo-Differential Operators and Applications
IS - 2
ER -