An algebra of pseudodifferential operators and the asymptotics of quantum mechanics
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Publication:1249752
DOI10.1016/0022-1236(78)90049-6zbMath0386.47031OpenAlexW2025323038MaRDI QIDQ1249752
Publication date: 1978
Published in: Journal of Functional Analysis (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/0022-1236(78)90049-6
Groups and semigroups of linear operators, their generalizations and applications (47D99) Integral, integro-differential, and pseudodifferential operators (47Gxx)
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Cites Work
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- General concept of quantization
- Mathematical characterization of the physical vacuum for a linear Bose- Einstein field
- An evolution equation in phase space and the Weyl correspondence
- Sur certains groupes d'opérateurs unitaires
- Quantization from the algebraic viewpoint
- Oscillatory integrals, lagrange immersions and unfolding of singularities
- Mathematical Aspects of the Weyl Correspondence
- An algebra of pseudo‐differential operators
- Dirac Formalism and Symmetry Problems in Quantum Mechanics. I. General Dirac Formalism
- Distributions and Their Hermite Expansions
- On the principles of elementary quantum mechanics