A sufficient nonsingularity condition for a discrete finite-gap one-energy two-dimensional Schrödinger operator on the quad-graph

DOI10.1007/s10688-015-0106-zzbMath1330.81099OpenAlexW1951447327MaRDI QIDQ903413

B. O. Vasilevskii

Publication date: 6 January 2016

Published in: Functional Analysis and its Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10688-015-0106-z

zbMATH Keywords

Riemann surfacespectral curvediscrete operatordiscrete complex analysisnonsingularityM-curvefinite-gap operator

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Discrete version of topics in analysis (39A12) Relationships between algebraic curves and integrable systems (14H70) Graph theory (05C99) Relationships between algebraic curves and physics (14H81) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35)

Cites Work

• Integrable discrete Schrödinger equations and a characterization of Prym varieties by a pair of quadrisecants
• Theta functions on Riemann surfaces
• Integrable lattices and their sublattices: From the discrete Moutard (discrete Cauchy-Riemann) 4-point equation to the self-adjoint 5-point scheme
• Linear and nonlinear theories of discrete analytic functions. Integrable structure and isomonodromic Green’s function
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