On the exact WKB analysis of operators admitting infinitely many phases.

DOI10.1016/S0001-8708(03)00049-5zbMath1056.34103MaRDI QIDQ1421397

Takashi Aoki, Takahiro Kawai, Yoshitsugu Takei, Tatsuya Koike

Publication date: 26 January 2004

Published in: Advances in Mathematics (Search for Journal in Brave)

zbMATH Keywords

Turning pointConnection formulaExact WKB analysisInfinitely many phasesOperator of WKB typeStokes curve

Mathematics Subject Classification ID

Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Singular perturbations, turning point theory, WKB methods for ordinary differential equations (34E20) Singular perturbation problems for ordinary differential equations in the complex domain (complex WKB, turning points, steepest descent) (34M60)

Related Items

On the Stokes geometry of perturbed tangential Pearcey systems ⋮ Degeneration structure of the Voros coefficients of the generalized hypergeometric differential equations with a large parameter ⋮ Quantization of complex Lagrangian submanifolds ⋮ On infinite order and fully nonlinear partial differential evolution equations ⋮ A modification of \(\mathsf {WKB}\) method for fractional differential operators of Schrödinger's type ⋮ Exact WKB Analysis of Eigenvalue Problems for an Ordinary Differential Equation Arising from the Mathematical Model of Mesons ⋮ On the exact WKB analysis of higher order simple-pole type operators ⋮ On parametric Gevrey asymptotics for initial value problems with infinite order irregular singularity and linear fractional transforms ⋮ Exact WKB and abelianization for the \(T_3\) equation ⋮ WKB Analysis and Stokes Geometry of Differential Equations ⋮ On the exact WKB analysis of microdifferential operators of WKB type. ⋮ Classification of deformation quantization algebroids on complex symplectic manifolds ⋮ Voros coefficients at the origin and at the infinity of the generalized hypergeometric differential equations with a large parameter

Cites Work

• Calcul exponential des opérateurs microdifférentiels d'ordre infini. II
• Calcul exponentiel des opérateurs microdifférentiel d'ordre infini. I
• Voros resurrection and periods of hyperelliptic curves
• Microlocal reduction of ordinary differential operators with a large parameter
• On the exact WKB analysis for the third order ordinary differential equations with a large parameter
• Quantized contact transformations and pseudodifferential operators of infinite order
• Stability of electrostatic drift waves in bumpy tori
• WKB method for systems of integral equations
• New Stokes’ line in WKB theory
• Idéaux de fonctions analytiques de $n$ variables complexes
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item