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

• Published in: Geometric and functional analysis Vol. 26; no. 1; pp. 288 - 305
• Main Authors: Laptev, Ari, Schimmer, Lukas, Takhtajan, Leon A.
• Format: Journal Article
• Language: English
• Published: Cham Springer International Publishing 01.02.2016
• Subjects: Analysis; Mathematics; Mathematics and Statistics; Tauberian Theorem; Trace Class; Dehn Twist; Topological String; Coherent State

We investigate Weyl type asymptotics of functional-difference operators associated to mirror curves of special del Pezzo Calabi-Yau threefolds. These operators are H ( ζ ) = U + U - 1 + V + ζ V - 1 and H m , n = U + V + q - m n U - m V - n , where U and V are self-adjoint Weyl operators satisfying U...