Exact constructions of square-root Helmholtz operator symbols: The focusing quadratic profile
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Publication:2738089
DOI10.1063/1.533384zbMath1044.35017OpenAlexW2038626208MaRDI QIDQ2738089
Maarten V. de Hoop, Louis Fishman, Mattheus J. N. van Stralen
Publication date: 30 August 2001
Published in: Journal of Mathematical Physics (Search for Journal in Brave)
Full work available at URL: https://semanticscholar.org/paper/8fb2283881ac0f54e8a36d39ee8fd1f0bc7373b3
Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Representations of solutions to partial differential equations (35C99) Pseudodifferential operators and other generalizations of partial differential operators (35S99)
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Cites Work
- Phase space methods and path integration: the analysis and computation of scalar wave equations
- Uniform high-frequency approximations of the square root Helmholtz operator symbol
- A rigorous path integral construction in any dimension
- PARABOLIC EQUATION DEVELOPMENT IN RECENT DECADE
- The uncertainty principle
- Derivation and application of extended parabolic wave theories. I. The factorized Helmholtz equation
- Derivation and application of extended parabolic wave theories. II. Path integral representations
- Explicit time-dependent Schrodinger propagators
- Exact and operator rational approximate solutions of the Helmholtz, Weyl composition equation in underwater acoustics−The quadratic profile
- The weyl calculus of pseudo-differential operators
- Uniform Asymptotic Expansion of the Generalized Bremmer Series
- Horizontal ray theory for ocean acoustics
- A new perspective on functional integration
- Generalization of the Bremmer coupling series
- Generalization of the phase-screen approximation for the scattering of acoustic waves.
