An application of the inverse scattering problem for the discrete Dirac operator

Aleskerov, Rza I.

doi:10.29228/proc.20

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2021

2023

Publication Types

Select...

Article1

Other1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“….79) so, applying (4.70) to the (u h ) h on the right hand side of (4.79) and multiplying the both sides of (4.79) by1 m−z (D m,h − z) −1 , we infer that…”

mentioning

confidence: 99%

Continuum limits for discrete Dirac operators on 2D square lattices

Schmidt

Umeda

2023

Anal.Math.Phys.

View full text Add to dashboard Cite

We discuss the continuum limit of discrete Dirac operators on the square lattice in $${\mathbb {R}}^2$$ R 2 as the mesh size tends to zero. To this end, we propose the most natural and simplest embedding of $$\ell ^2({\mathbb {Z}}_h^d)$$ ℓ 2 ( Z h d ) into $$L^2({\mathbb {R}}^d)$$ L 2 ( R d ) , which enables us to compare the discrete Dirac operators with the continuum Dirac operators in the same Hilbert space $$L^2({\mathbb {R}}^2)^2$$ L 2 ( R 2 ) 2 . In particular, we prove that the discrete Dirac operators converge to the continuum Dirac operators in the strong resolvent sense. Potentials are assumed to be bounded and uniformly continuous functions on $${\mathbb {R}}^2$$ R 2 and allowed to be complex matrix-valued. We also prove that the discrete Dirac operators do not converge to the continuum Dirac operators in the norm resolvent sense. This is closely related to the observation that the Liouville theorem does not hold in discrete complex analysis.

show abstract

“….79) so, applying (4.70) to the (u h ) h on the right hand side of (4.79) and multiplying the both sides of (4.79) by1 m−z (D m,h − z) −1 , we infer that…”

mentioning

confidence: 99%