Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves

DOI10.1007/s00039-016-0357-8zbMath1361.47004arXiv1510.00045OpenAlexW2964069050MaRDI QIDQ295851

Lukas Schimmer, A. A. Laptev, L. A. Takhtadzhyan

Publication date: 14 June 2016

Published in: Geometric and Functional Analysis. GAFA (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.00045

zbMATH Keywords

eigenvaluespectrumWeyl operatorWeyl asymptoticsCalabi-Yau threefold

Mathematics Subject Classification ID

Calabi-Yau manifolds (algebro-geometric aspects) (14J32) Spectrum, resolvent (47A10) Linear symmetric and selfadjoint operators (unbounded) (47B25) (3)-folds (14J30) Difference operators (39A70) Linear difference operators (47B39) Relationships between algebraic curves and physics (14H81)

Related Items (22)

A solvable deformation of quantum mechanics ⋮ Global regularity of Weyl pseudo-differential operators with radial symbols in each phase-space variable ⋮ Operators and higher genus mirror curves ⋮ Exact eigenfunctions and the open topological string ⋮ Spectral determinants and quantum theta functions ⋮ Etudes of the resolvent ⋮ Thermal entropy in Calabi-Yau quantum mechanics ⋮ High order perturbation theory for difference equations and Borel summability of quantum mirror curves ⋮ Non-perturbative approaches to the quantum Seiberg-Witten curve ⋮ Spectral theory and mirror symmetry ⋮ Non-perturbative quantum mechanics from non-perturbative strings ⋮ New results in \(\mathcal N=2\) theories from non-perturbative string ⋮ Equivalent Hamiltonian approach to quantum cosmology of integrable models ⋮ Weyl asymptotics for perturbed functional difference operators ⋮ Infinite order \(\Psi\mathrm{DOs}\): composition with entire functions, new Shubin-Sobolev spaces, and index theorem ⋮ Trace formulas for the modified Mathieu equation ⋮ A sharp Lieb-Thirring inequality for functional difference operators ⋮ Infinite Order Pseudo-Differential Operators ⋮ Wavefunctions, integrability, and open strings ⋮ Quantized mirror curves and resummed WKB ⋮ The complex side of the TS/ST correspondence ⋮ Quantum curves and \(q\)-deformed Painlevé equations

Cites Work

• Operators from mirror curves and the quantum dilogarithm
• Topological strings from quantum mechanics
• Nonclassical eigenvalue asymptotics
• Topological strings and integrable hierarchies
• Dirichlet and Neumann eigenvalue problems on domains in Euclidean spaces
• Neuer Beweis und Verallgemeinerung einiger Tauberian-Sätze
• The classical limit of quantum spin systems
• The spectral theory of a functional-difference operator in conformal field theory
• COVARIANT AND CONTRAVARIANT SYMBOLS OF OPERATORS
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