Representation of Bessel functions by the Maslov canonical operator

DOI10.1134/S0040577921080031zbMath1471.81033OpenAlexW3193330868MaRDI QIDQ2047692

S. Yu. Dobrokhotov, D. S. Minenkov, Vladimir E. Nazaikinskii

Publication date: 23 August 2021

Published in: Theoretical and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0040577921080031

zbMATH Keywords

semiclassical asymptoticsWKB approximationBessel functioncanonical operator

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Semiclassical techniques, including WKB and Maslov methods applied to problems in quantum theory (81Q20) Bessel and Airy functions, cylinder functions, ({}_0F_1) (33C10) Canonical quantization (81S08)

Related Items

New integral representations for the Maslov canonical operator on an isotropic manifold with a complex germ ⋮ Internal gravity waves from a localized source in stratified medium flow with a model buoyancy frequency distribution ⋮ Semiclassical theory for plasmons in spatially inhomogeneous media

Cites Work

• Maslov's canonical operator in arbitrary coordinates on the Lagrangian manifold
• New formulas for Maslov's canonical operator in a neighborhood of focal points and caustics in two-dimensional semiclassical asymptotics
• Lagrangian manifolds related to the asymptotics of Hermite polynomials
• Representations of rapidly decaying functions by the Maslov canonical operator
• Reduction of symplectic manifolds with symmetry
• Simple asymptotics for a generalized wave equation with degenerating velocity and their applications in the linear long wave run-up problem
• Uniform asymptotic solution in the form of an Airy function for semiclassical bound states in one-dimensional and radially symmetric problems
• Uniformization of equations with Bessel-type boundary degeneration and semiclassical asymptotics
• Lagrangian manifolds and efficient short-wave asymptotics in a neighborhood of a caustic cusp
• Maslov's canonical operator, Hörmander's formula, and localization of the Berry-Balazs solution in the theory of wave beams
• The Maslov canonical operator on Lagrangian manifolds in the phase space corresponding to a wave equation degenerating on the boundary
• MATLAB kompakt
• New integral representations of the Maslov canonical operator in singular charts
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item