Abstract
When Iz Singer called to invite me to give a lecture at this symposium I was very doubtful since I did not see that anything I had been thinking of recently was related to the work of Norbert Wiener. However, I quickly realised when browsing through the collected works that I had underestimated the wide scope of his work, for there is a paper [Wie] which is connected with a recent paper of mine [H].
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References
[AH] J. E. Avron and I. Herbst, Spectral and scattering theory of Schrödinger operators related to the Stark effect, Comm. Math. Phys. 52 (1977), 239–254.
[D] Jan Derezinski, Some remarks on Weyl pseudo-differential operators, Journées “Equations aux dérivées partielles” Saint-Jean-de Monts 1993, Exp. XII.
[H] L. Hörmander, Symplectic classification of quadratic forms, and general Mehler formulas, Math. Z. (to appear).
[L] E. H. Lieb, Gaussian kernels have only Gaussian maximizers, Inv. Math. 102 (1990), 179–208.
[M] E. Mehler, Reihenentwicklungen nach Laplaceschen Funktionen höherer Ordnung, J. Reine Angew. Math. 66 (1866), 161–176.
[S] I. Segal, Transforms for operators and symplectic automorphisms over a locally compact abelian group, Math. Scand. 13 (1963), 31–43.
[Wey] H. Weyl, Quantenmechanik und Gruppentheorie, Zeitschrift für Physik 46 (1927), 1–47, Collected works, Vol. III, pp. 90–135.
[Wie] N. Wiener, Hermitian polynomials and Fourier analysis, J. Math. and Phys. 8 (1929), 70–73, Collected works Vol. II, pp. 914–918.
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Hörmander, L. (2018). General Mehler Formulas And The Weyl Calculus. In: Unpublished Manuscripts . Springer, Cham. https://doi.org/10.1007/978-3-319-69850-2_21
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DOI: https://doi.org/10.1007/978-3-319-69850-2_21
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