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Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)
     

The uncertainty principle

Author(s): Charles L. Fefferman
Journal: Bull. Amer. Math. Soc. 9 (1983), 129-206.
MSC (1980): Primary 35-02, 35H05, 35P15, 35S05, 42B20, 42B25, 81H05
MathSciNet review: 707957
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References:

1.
R. Beals and C. Fefferman, On local solvability of partial differential equations, Ann. of Math. (2) 97 (1973), 552-571. MR 352746
2.
R. Beals and C. Fefferman, Spatially inhomogenous pseudodifferential operators, Comm. Pure Appl. Math. 27 (1974), 1-24. MR 352747
3.
M. Beals, C. Fefferman and R. Grossman, Strictly pseudoconvex domains in C, Bull. Amer. Math. Soc. (N.S.) 8 (1983), 125-322. MR 684898
4.
A. Calderón and R. Vaillancourt, A class of bounded pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A. 69 (1972), 1185-1187. MR 298480
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.
7.
S. Cheng and S.-T. Yau, On the existence of complete Kähler metric on noncompact manifolds and the regularity of Fefferman's equation, Comm. Pure Appl. Math. 33 (1980), 507-544. MR 575736
8.
A. Cordoba and C. Fefferman, Wave packets and Fourier integral operators, Comm. Partial Differential Equations 3 (11) (1978), 979-1005. MR 507783
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.

10.
Yu. V. Egorov, Subelliptic operators, Uspekhi Mat. Nauk. 30 (1975), 57-104; English transl, Russian Math. Surveys 30 (1975). MR 410474
11.
C. Fefferman, Recent progress in classical Fourier analysis, Proc. Internat. Congress Math. (Vancouver, 1974), Vol. 1, Canad. Math. Congr., Montreal, Que., 1975, pp. 95-118. MR 510853
12.
C. Fefferman, The Bergman kernel and biholomorphic mappings of pseudoconvex domains, Invent. Math. 26 (1974), 1-66. MR 350069
13.
C. Fefferman and D. H. Phong, On positivity of pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A. 75 (1978), 4673-4674. MR 507931
14.
C. Fefferman and D. H. Phong, The uncertainty principle and sharp Gårding inequalities, Comm. Pure Appl. Math. 34 (1981), 285-331. MR 611747
15.
C. Fefferman and D. H. Phong, On the asymptotic eigenvalue distribution of a pseudodifferential operator, Proc. Nat. Acad. Sci. U.S.A. 77 (1980), 5622-5625. MR 589278
16.
C. Fefferman and D. H. Phong, Subelliptic eigenvalue problems, Conf. in Honor of A. Zygmund. (W. Beckner et al, eds.), Wadsworth Math. Series, 1981. MR 730094
17.
C. Fefferman and D. H. Phong, Symplectic geometry and positivity of pseudodifferential operators, Proc. Nat. Acad. Sci. U.S.A. 79 (1982), 710-713. MR 648064
18.
R. Fefferman, personal communication.
19.
G. Folland and E. M. Stein, Estimates for the $\bar \partial \sbb$ complex and analysis on the Heisenberg group, Comm. Pure Appl. Math. 27 (1974), 429-522. MR 367477
20.
R. Greiner and E. M. Stein, Estimates for the $øverline\partial$-Neumann problem, Math. Notes 19 (1977).
21.
R. Hunt, An extension of the Marcinkiewicz interpolation theorem, Bull. Amer. Math. Soc. 70 (1964), 803-807. MR 169037
22.
L. Hörmander, Hypoelliptic second-order differential equations, Acta Math. 119 (1967), 147-171. MR 222474
23.
L. Hörmander, The spectral function of an elliptic operator, Acta Math. 121 (1968), 192-218. MR 609014
24.
L. Hörmander, Subelliptic operators, Seminar on Singularities of Solutions of Linear Partial Differential Equations, Princeton Univ. Press, Princeton, N.J., 1979. 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.
26.
J. J. Kohn, Harmonic integrals on strongly pseudoconvex manifolds. I, II, Ann. of Math. (2) 78 (1963), 206-213; ibid. 79 (1964), 450-472. MR 208200
27.
J. J. Kohn, Subellipticity of the $\bar \partial $-Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79-122. MR 512213
28.
A. Kolmogorov, Zufällige Bewegungen, Ann. of Math. (2) 35 (1934), 116-117. MR 1503147
29.
R. Lee and R. Melrose, to appear.
30.
E. Lieb, Stability of matter, Rev. Modern Phys. 48 (1976), 553-569. MR 456083
31.
R. Moyer, On the Nirenberg-Treves condition for local solvability, J. Differential Equations 26 (1977), 223-239. MR 460857
32.
A. Nagel, E. M. Stein and S. Wainger, to appear.
33.
L. Nirenberg and F. Trèves, Solvability of a first-order linear partial differential equation, Comm. Pure Appl. Math. 16 (1963), 331-351. MR 163045
34.
L. Nirenberg and F. Trèves, On local solvability of linear partial differential equations. I: Necessary conditions; II: Sufficient conditions, Comm. Pure Appl. Math. 23 (1970), 1-38; 459-509. MR 264470
35.
O. Oleinik and E. Radkevitch, Second-order equations with non-negative characteristic form.
36.
D. Phong, On integral representations of the Neumann operator, Proc. Nat. Acad. Sci. U.S.A. 76 (1979), 1554-1558. MR 526179
37.
L. Rothschild and E. M. Stein, Hypoelliptic differential operators and nilpotent groups, Acta Math. 137 (1976), 247-320. MR 436223
38.
A. Sanchez, Estimates for kernels associated to some subelliptic operators, Thesis, Princeton Univ., 1983.
39.
B. Simon, to appear.
40.
B. Simon, Functional integration and quantum physics, Academic Press, 1979. MR 544188
41.
H. Weyl, Ramifications, old and new, of the eigenvalue problem, Bull. Amer. Math. Soc. 56 (1950), 115-139. MR 34940

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Additional Information:

DOI: 10.1090/S0273-0979-1983-15154-6
PII: S 0273-0979(1983)15154-6


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