The uncertainty principle
Author:
Charles L. Fefferman
Journal:
Bull. Amer. Math. Soc. 9 (1983), 129-206
MSC (1980):
Primary 35-02, 35H05, 35P15, 35S05, 42B20, 42B25, 81H05
DOI:
https://doi.org/10.1090/S0273-0979-1983-15154-6
Remark:
Proc. Amer. Math. Soc. 108, no. 2 (1990), pp. 407-409.
MathSciNet review:
707957
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- Richard Beals and Charles Fefferman, On local solvability of linear partial differential equations, Ann. of Math. (2) 97 (1973), 482–498. MR 352746, DOI https://doi.org/10.2307/1970832
- Richard Beals and Charles Fefferman, Spatially inhomogeneous pseudodifferential operators. I, Comm. Pure Appl. Math. 27 (1974), 1–24. MR 352747, DOI https://doi.org/10.1002/cpa.3160270102
- Michael Beals, Charles Fefferman, and Robert Grossman, Strictly pseudoconvex domains in ${\bf C}^{n}$, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 2, 125–322. MR 684898, DOI https://doi.org/10.1090/S0273-0979-1983-15087-5
- Alberto-P. Calderón and Rémi Vaillancourt, A class of bounded pseudo-differential operators, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185–1187. MR 298480, DOI https://doi.org/10.1073/pnas.69.5.1185 5. T. Carleman, Complete works (A. Pleijel et al, eds.), Malmo Litös, 1960. 6. D. Catlin, Necessary conditions for subelliptiticy and hypoellipticity for the $øverline\partial$-Neumann problem on pseudoconvex domains, Recent Developments in Several Complex Variables, Ann. of Math. Stud., no. 100, 1981.
- Shiu Yuen Cheng and Shing Tung Yau, On the existence of a complete Kähler metric on noncompact complex manifolds and the regularity of Fefferman’s equation, Comm. Pure Appl. Math. 33 (1980), no. 4, 507–544. MR 575736, DOI https://doi.org/10.1002/cpa.3160330404
- Antonio Córdoba and Charles Fefferman, Wave packets and Fourier integral operators, Comm. Partial Differential Equations 3 (1978), no. 11, 979–1005. MR 507783, DOI https://doi.org/10.1080/03605307808820083 9. J. D’Angelo, Real hypersurfaces with degenerate Levi form, Thesis, Princeton Univ., Princeton, N.J., 1976. 9a. F. Dyson and A. Lenard, Stability of matter. I, J. Math. Phys. 8 (1967), 423-434.
- Ju. V. Egorov, Subelliptic operators, Uspehi Mat. Nauk 30 (1975), no. 3(183), 57–104 (Russian). MR 0410474
- Charles Fefferman, Recent progress in classical Fourier analysis, Proceedings of the International Congress of Mathematicians (Vancouver, B.C., 1974) Canad. Math. Congress, Montreal, Que., 1975, pp. 95–118. MR 0510853
- Charles Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1–65. MR 350069, DOI https://doi.org/10.1007/BF01406845
- C. Fefferman and D. H. Phong, On positivity of pseudo-differential operators, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), no. 10, 4673–4674. MR 507931, DOI https://doi.org/10.1073/pnas.75.10.4673
- C. Fefferman and D. H. Phong, The uncertainty principle and sharp Gȧrding inequalities, Comm. Pure Appl. Math. 34 (1981), no. 3, 285–331. MR 611747, DOI https://doi.org/10.1002/cpa.3160340302
- C. Fefferman and D. H. Phong, On the asymptotic eigenvalue distribution of a pseudodifferential operator, Proc. Nat. Acad. Sci. U.S.A. 77 (1980), no. 10, 5622–5625. MR 589278, DOI https://doi.org/10.1073/pnas.77.10.5622
- C. Fefferman and D. H. Phong, Subelliptic eigenvalue problems, Conference on harmonic analysis in honor of Antoni Zygmund, Vol. I, II (Chicago, Ill., 1981) Wadsworth Math. Ser., Wadsworth, Belmont, CA, 1983, pp. 590–606. MR 730094
- C. Fefferman and D. H. Phong, Symplectic geometry and positivity of pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), no. 2, 710–713. MR 648064, DOI https://doi.org/10.1073/pnas.79.2.710 18. R. Fefferman, personal communication.
- G. B. Folland and E. M. Stein, Estimates for the $\bar \partial _{b}$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429–522. MR 367477, DOI https://doi.org/10.1002/cpa.3160270403 20. R. Greiner and E. M. Stein, Estimates for the $øverline\partial$-Neumann problem, Math. Notes 19 (1977).
- Richard A. Hunt, An extension of the Marcinkiewicz interpolation theorem to Lorentz spaces, Bull. Amer. Math. Soc. 70 (1964), 803–807. MR 169037, DOI https://doi.org/10.1090/S0002-9904-1964-11242-8
- Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI https://doi.org/10.1007/BF02392081
- Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. MR 609014, DOI https://doi.org/10.1007/BF02391913
- Lars Hörmander, Subelliptic operators, Seminar on Singularities of Solutions of Linear Partial Differential Equations (Inst. Adv. Study, Princeton, N.J., 1977/78) Ann. of Math. Stud., vol. 91, Princeton Univ. Press, Princeton, N.J., 1979, pp. 127–208. MR 547019 25. D. Iagolnitzer, Appendix: Microlocal essential support of a distribution and decomposition theorems —an introduction, Lecture Notes in Math., Vol. 449, Springer-Verlag, 1975, pp. 121-132.
- J. J. Kohn, Harmonic integrals on strongly pseudo-convex manifolds. II, Ann. of Math. (2) 79 (1964), 450–472. MR 208200, DOI https://doi.org/10.2307/1970404
- J. J. Kohn, Subellipticity of the $\bar \partial $-Neumann problem on pseudo-convex domains: sufficient conditions, Acta Math. 142 (1979), no. 1-2, 79–122. MR 512213, DOI https://doi.org/10.1007/BF02395058
- A. Kolmogoroff, Zufällige Bewegungen (zur Theorie der Brownschen Bewegung), Ann. of Math. (2) 35 (1934), no. 1, 116–117 (German). MR 1503147, DOI https://doi.org/10.2307/1968123 29. R. Lee and R. Melrose, to appear.
- Elliott H. Lieb, The stability of matter, Rev. Modern Phys. 48 (1976), no. 4, 553–569. MR 0456083, DOI https://doi.org/10.1103/RevModPhys.48.553
- R. D. Moyer, On the Nirenberg-Treves condition for local solvability, J. Differential Equations 26 (1977), no. 2, 223–239. MR 460857, DOI https://doi.org/10.1016/0022-0396%2877%2990192-9 32. A. Nagel, E. M. Stein and S. Wainger, to appear.
- L. Nirenberg and F. Treves, Solvability of a first order linear partial differential equation, Comm. Pure Appl. Math. 16 (1963), 331–351. MR 163045, DOI https://doi.org/10.1002/cpa.3160160308
- Louis Nirenberg and François Trèves, On local solvability of linear partial differential equations. I. Necessary conditions, Comm. Pure Appl. Math. 23 (1970), 1–38. MR 264470, DOI https://doi.org/10.1002/cpa.3160230102 35. O. Oleinik and E. Radkevitch, Second-order equations with non-negative characteristic form.
- D. H. Phong, On integral representations for the Neumann operator, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), no. 4, 1554–1558. MR 526179, DOI https://doi.org/10.1073/pnas.76.4.1554
- Linda Preiss Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), no. 3-4, 247–320. MR 436223, DOI https://doi.org/10.1007/BF02392419 38. A. Sanchez, Estimates for kernels associated to some subelliptic operators, Thesis, Princeton Univ., 1983. 39. B. Simon, to appear.
- Barry Simon, Functional integration and quantum physics, Pure and Applied Mathematics, vol. 86, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1979. MR 544188
- Hermann Weyl, Ramifications, old and new, of the eigenvalue problem, Bull. Amer. Math. Soc. 56 (1950), 115–139. MR 34940, DOI https://doi.org/10.1090/S0002-9904-1950-09369-0
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