The uncertainty principle
HTML articles powered by AMS MathViewer
- by Charles L. Fefferman PDF
- Bull. Amer. Math. Soc. 9 (1983), 129-206
References
- Richard Beals and Charles Fefferman, On local solvability of linear partial differential equations, Ann. of Math. (2) 97 (1973), 482–498. MR 352746, DOI 10.2307/1970832
- Richard Beals and Charles Fefferman, Spatially inhomogeneous pseudodifferential operators. I, Comm. Pure Appl. Math. 27 (1974), 1–24. MR 352747, DOI 10.1002/cpa.3160270102
- Michael Beals, Charles Fefferman, and Robert Grossman, Strictly pseudoconvex domains in $\textbf {C}^{n}$, Bull. Amer. Math. Soc. (N.S.) 8 (1983), no. 2, 125–322. MR 684898, DOI 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 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 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 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 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 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 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 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 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 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 10.1090/S0002-9904-1964-11242-8
- Lars Hörmander, Hypoelliptic second order differential equations, Acta Math. 119 (1967), 147–171. MR 222474, DOI 10.1007/BF02392081
- Lars Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 193–218. MR 609014, DOI 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 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 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 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 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 10.1016/0022-0396(77)90192-9 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 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 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 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 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 10.1090/S0002-9904-1950-09369-0
Additional Information
- 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
- MathSciNet review: 707957