The Weyl transform and $L^ p$ functions on phase space
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- by Barry Simon PDF
- Proc. Amer. Math. Soc. 116 (1992), 1045-1047 Request permission
Abstract:
This is primarily a negative paper showing that a bound of the form $||W(f)||{\text {operator norm}} \leq c||f|{|_p}$ fails for the Weyl transform if $p > 2$. ${L^p}$ properties of Wigner distribution functions are discussed as well as Cwikel’s theorem.References
- A. Grossmann, G. Loupias, and E. M. Stein, An algebra of pseudodifferential operators and quantum mechanics in phase space, Ann. Inst. Fourier (Grenoble) 18 (1968), no. fasc. 2, 343–368, viii (1969) (English, with French summary). MR 267425, DOI 10.5802/aif.305
- Abel Klein and Bernard Russo, Sharp inequalities for Weyl operators and Heisenberg groups, Math. Ann. 235 (1978), no. 2, 175–194. MR 499945, DOI 10.1007/BF01405012
- James C. T. Pool, Mathematical aspects of the Weyl correspondence, J. Mathematical Phys. 7 (1966), 66–76. MR 204049, DOI 10.1063/1.1704817
- Barry Simon, Trace ideals and their applications, London Mathematical Society Lecture Note Series, vol. 35, Cambridge University Press, Cambridge-New York, 1979. MR 541149, DOI 10.1007/BFb0064579
Additional Information
- © Copyright 1992 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 116 (1992), 1045-1047
- MSC: Primary 81S30; Secondary 47B38
- DOI: https://doi.org/10.1090/S0002-9939-1992-1100663-7
- MathSciNet review: 1100663