The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Fourier integral operators. I
Abstract
Pseudo-differential operators have been developed as a tool for the study of elliptic differential equations.Suitably extended versions are also applicable to hypoelliptic equations, but their value is rather limited in genuinely non-elliptic problems.In this paper we shall therefore discuss some more general classes of operators which are adapted to such applications.For these operators we shall develop a calculus which is almost as smooth as that of pseudo-differential operators.It also seems that one gains some more insight into the theory of pseudo-differential operators by considering them from the point of view of the wider classes of operators to be discussed here so we shall take the opportunity to include a short exposition.
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Cites
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L'intégrale de Riemann-Liouville et le problème de Cauchy
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Duistermaat, J. J., & Heckman, G. J. (1982) · Inventiones Mathematicae · doi:10.1007/bf01399506 · Cited by 744
Solving inverse problems using data-driven models
Arridge, S., Maass, P., Öktem, O., & Schönlieb, C.-B. (2019) · Acta Numerica · doi:10.1017/s0962492919000059 · Cited by 686
Uniform distribution of eigenfunctions on compact hyperbolic surfaces
Zelditch, S. (1987) · Duke Mathematical Journal · doi:10.1215/s0012-7094-87-05546-3 · Cited by 549
A Semiclassical Approach to the Dirac Equation
Bolte, J., & Keppeler, S. (1999) · Annals of Physics · doi:10.1006/aphy.1999.5912 · Cited by 135
A general worldline quantum inequality
Fewster, C. J. (1999) · arXiv · doi:10.48550/arxiv.gr-qc/9910060 · Cited by 134
Geometry of the transport equation in multicomponent WKB approximations
Emmrich, C., & Weinstein, A. (1996) · Communications in Mathematical Physics · doi:10.1007/bf02099256 · Cited by 89
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Calcagni, G., & Nardelli, G. (2025) · Chaos, Solitons & Fractals · doi:10.1016/j.chaos.2025.117401 · Cited by 7
Metadata
- Authors
- Hörmander, L.
- Venue
- Acta Mathematica
- Publisher
- International Press of Boston
- Published
- 1971
- Volume
- 127
- Issue
- 0
- Pages
- 79-183
- ISSN
- 0001-5962 (ISSN-L)
- OpenAlex
- W2016716371
- Cited by
- 2,306
- References
- 24
- FWCI
- 26.63
- Type
- journal article
- Language
- en
- Open access
- closed
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