Weyl Type Asymptotics and Bounds for the Eigenvalues of Functional-Difference Operators for Mirror Curves

@article{Laptev2015WeylTA,
  title={Weyl Type Asymptotics and Bounds for the Eigenvalues of Functional-Difference Operators for Mirror Curves},
  author={Ari Laptev and Lukas Schimmer and Leon A. Takhtajan},
  journal={Geometric and Functional Analysis},
  year={2015},
  volume={26},
  pages={288-305}
}
  • Ari Laptev, Lukas Schimmer, Leon A. Takhtajan
  • Published 2015
  • Mathematics, Physics
  • Geometric and Functional Analysis
  • We investigate Weyl type asymptotics of functional-difference operators associated to mirror curves of special del Pezzo Calabi-Yau threefolds. These operators are $${H(\zeta) = U + U^{-1} + V + \zeta V^{-1}}$$H(ζ)=U+U-1+V+ζV-1 and $${H_{m,n} = U + V + q^{-mn}U^{-m}V^{-n}}$$Hm,n=U+V+q-mnU-mV-n, where $${U}$$U and $${V}$$V are self-adjoint Weyl operators satisfying $${UV = q^{2}VU}$$UV=q2VU with $${q = {\rm e}^{{\rm i}\pi b^{2}}}$$q=eiπb2, $${b > 0}$$b>0 and $${\zeta > 0}$$ζ>0, $${m, n \in… CONTINUE READING