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Volumn 201, Issue 1, 2001, Pages 19-60

Conformally invariant non-local operators

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EID: 0038438092     PISSN: 00308730     EISSN: None     Source Type: Journal    
DOI: 10.2140/pjm.2001.201.19     Document Type: Article
Times cited : (35)

References (48)
  • 1
    • 84881278049 scopus 로고
    • The Thomas structure bundle for conformal, projective and related structures
    • MR 96e:53016, Zbl 828.53012
    • T.N. Bailey, M.G. Eastwood and A.R. Gover, The Thomas structure bundle for conformal, projective and related structures, Rocky Mountain Journal of Math., 24 (1994), 1191-1217, MR 96e:53016, Zbl 828.53012.
    • (1994) Rocky Mountain Journal of Math. , vol.24 , pp. 1191-1217
    • Bailey, T.N.1    Eastwood, M.G.2    Gover, A.R.3
  • 2
    • 84972507728 scopus 로고
    • Verma modules and differential conformal invariants
    • MR 92a:58151, Zbl 732.53011
    • R. Baston, Verma modules and differential conformal invariants, J. Diff. Geom., 32 (1990) 851-898, MR 92a:58151, Zbl 732.53011.
    • (1990) J. Diff. Geom. , vol.32 , pp. 851-898
    • Baston, R.1
  • 4
    • 84960568389 scopus 로고
    • The transformation of the electrodynamical equations
    • H. Bateman, The transformation of the electrodynamical equations, Proc. London Math. Soc., 8 (1910), 223-264.
    • (1910) Proc. London Math. Soc. , vol.8 , pp. 223-264
    • Bateman, H.1
  • 5
    • 0000759151 scopus 로고
    • Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality
    • MR 94m:58232, Zbl 826.58042
    • W. Beckner, Sharp Sobolev inequalities on the sphere and the Moser-Trudinger inequality, Annals of Math., 138 (1993), 213-242, MR 94m:58232, Zbl 826.58042.
    • (1993) Annals of Math. , vol.138 , pp. 213-242
    • Beckner, W.1
  • 6
    • 84924408006 scopus 로고
    • Conformally covariant equations on differential forms
    • MR 84g:58110, Zbl 532.53021
    • T. Branson, Conformally covariant equations on differential forms, Commun. Partial Diff. Eq., 7 (1982), 393-431, MR 84g:58110, Zbl 532.53021.
    • (1982) Commun. Partial Diff. Eq. , vol.7 , pp. 393-431
    • Branson, T.1
  • 7
    • 0000815503 scopus 로고
    • Differential operators canonically associated to a conformal structure
    • MR 88a:58212, Zbl 596.53009
    • _, Differential operators canonically associated to a conformal structure, Math. Scand., 57 (1985), 293-345, MR 88a:58212, Zbl 596.53009.
    • (1985) Math. Scand. , vol.57 , pp. 293-345
  • 8
    • 0000327401 scopus 로고
    • Group representations arising from Lorentz conformal geometry
    • MR 90b:22016, Zbl 643.58036
    • _, Group representations arising from Lorentz conformal geometry, J. Funct. Anal., 74 (1987), 199-291, MR 90b:22016, Zbl 643.58036.
    • (1987) J. Funct. Anal. , vol.74 , pp. 199-291
  • 9
    • 0031574594 scopus 로고    scopus 로고
    • Stein-Weiss operators and ellipticity
    • MR 99b:58219, Zbl 904.58054
    • _, Stein-Weiss operators and ellipticity, J. Funct. Anal., 151 (1997), 334-383, MR 99b:58219, Zbl 904.58054.
    • (1997) J. Funct. Anal. , vol.151 , pp. 334-383
  • 10
    • 0039813814 scopus 로고    scopus 로고
    • Spectral theory of invariant operators, sharp inequalities, and representation theory
    • MR 98k:58237, Zbl 884.58100
    • _, Spectral theory of invariant operators, sharp inequalities, and representation theory, Supp. Rend. Circ. Matem. Palermo, 46 (1997), 29-54, MR 98k:58237, Zbl 884.58100.
    • (1997) Supp. Rend. Circ. Matem. Palermo , vol.46 , pp. 29-54
  • 11
    • 21144476884 scopus 로고
    • Estimates and extremals for zeta function determinants on four-manifolds
    • MR 93m:58116, Zbl 761.58053
    • T. Branson, S.-Y.A. Chang and P. Yang, Estimates and extremals for zeta function determinants on four-manifolds, Commun. Math. Phys., 149 (1992), 241-262, MR 93m:58116, Zbl 761.58053.
    • (1992) Commun. Math. Phys. , vol.149 , pp. 241-262
    • Branson, T.1    Chang, S.-Y.A.2    Yang, P.3
  • 12
    • 84953832735 scopus 로고
    • The asymptotics of the Laplacian on a manifold with boundary
    • MR 90m:58201, Zbl 721.58052
    • T. Branson and P. Gilkey, The asymptotics of the Laplacian on a manifold with boundary, Commun. Partial Diff. Eq., 15 (1990), 245-272, MR 90m:58201, Zbl 721.58052.
    • (1990) Commun. Partial Diff. Eq. , vol.15 , pp. 245-272
    • Branson, T.1    Gilkey, P.2
  • 13
    • 84966243066 scopus 로고
    • The functional determinant of a four-dimensional boundary-value problem
    • MR 94k:58155, Zbl 811.58060
    • _, The functional determinant of a four-dimensional boundary-value problem, Trans. Amer. Math. Soc., 344 (1994), 479-531, MR 94k:58155, Zbl 811.58060.
    • (1994) Trans. Amer. Math. Soc. , vol.344 , pp. 479-531
  • 14
    • 0030577617 scopus 로고    scopus 로고
    • Spectrum generating operators, and intertwining operators for representations induced from a maximal parabolic subgroup
    • MR 97g:22009, Zbl 841.22011
    • T. Branson, G. Ólafsson and B. Ørsted, Spectrum generating operators, and intertwining operators for representations induced from a maximal parabolic subgroup, J. Funct. Anal., 135 (1996), 163-205, MR 97g:22009, Zbl 841.22011.
    • (1996) J. Funct. Anal. , vol.135 , pp. 163-205
    • Branson, T.1    Ólafsson, G.2    ØRsted, B.3
  • 15
    • 0039681518 scopus 로고
    • Huyghens' principle in Riemannian symmetric spaces
    • MR 97f:58128, Zbl 822.43002
    • T. Branson, G. Ólafsson, and H. Schlichtkrull, Huyghens' principle in Riemannian symmetric spaces, Math. Ann., 301 (1995), 445-462, MR 97f:58128, Zbl 822.43002.
    • (1995) Math. Ann. , vol.301 , pp. 445-462
    • Branson, T.1    Ólafsson, G.2    Schlichtkrull, H.3
  • 17
    • 0031190439 scopus 로고    scopus 로고
    • The zeta functional determinants on manifolds with boundary, I, II
    • MR 98f:58199, Zbl 914.58039, Zbl 914.58040
    • S.-Y.A. Chang and J. Qing, The zeta functional determinants on manifolds with boundary, I, II, J. Funct. Anal., 147 (1997), 327-362 and 363-399, MR 98f:58199, Zbl 914.58039, Zbl 914.58040.
    • (1997) J. Funct. Anal. , vol.147 , pp. 327-362
    • Chang, S.-Y.A.1    Qing, J.2
  • 18
    • 0000270633 scopus 로고
    • Extremal metrics of zeta function determinants on 4-manifolds
    • MR 96e:58034, Zbl 842.58011
    • S.-Y.A. Chang and P. Yang, Extremal metrics of zeta function determinants on 4-manifolds, Annals of Math., 142 (1995), 171-212, MR 96e:58034, Zbl 842.58011.
    • (1995) Annals of Math. , vol.142 , pp. 171-212
    • Chang, S.-Y.A.1    Yang, P.2
  • 19
    • 0004261668 scopus 로고
    • Academic Press, San Diego, MR 95j:46063, Zbl 818.46076
    • A. Connes, Noncommutative Geometry, Academic Press, San Diego, 1994, MR 95j:46063, Zbl 818.46076.
    • (1994) Noncommutative Geometry
    • Connes, A.1
  • 20
    • 0000960072 scopus 로고
    • Wave equations in conformal space
    • MR 58 #32495, Zbl 014.08004
    • P.A.M. Dirac, Wave equations in conformal space, Ann. of Math., 37 (1936), 429-442, MR 58 #32495, Zbl 014.08004.
    • (1936) Ann. of Math. , vol.37 , pp. 429-442
    • Dirac, P.A.M.1
  • 21
    • 0002301675 scopus 로고    scopus 로고
    • Notes on conformal differential geometry
    • MR 98g:53021, Zbl 911.53020
    • M.G. Eastwood, Notes on conformal differential geometry, Supp. Rend. Circ. Matem. Palermo, 43 (1996), 57-76, MR 98g:53021, Zbl 911.53020.
    • (1996) Supp. Rend. Circ. Matem. Palermo , vol.43 , pp. 57-76
    • Eastwood, M.G.1
  • 22
    • 85037256849 scopus 로고    scopus 로고
    • Private communication
    • M.G. Eastwood, Private communication.
    • Eastwood, M.G.1
  • 23
    • 0001113939 scopus 로고
    • A conformally invariant Maxwell gauge
    • MR 86j:83031
    • M.G. Eastwood and M. Singer, A conformally invariant Maxwell gauge, Phys. Lett., 107A (1985), 73-74, MR 86j:83031.
    • (1985) Phys. Lett. , vol.107 A , pp. 73-74
    • Eastwood, M.G.1    Singer, M.2
  • 24
    • 84972534380 scopus 로고
    • The Yamabe problem on manifolds with boundary
    • MR 93b:53030, Zbl 771.53017
    • J. Escobar, The Yamabe problem on manifolds with boundary, J. Diff. Geom., 35 (1992), 21-84, MR 93b:53030, Zbl 771.53017.
    • (1992) J. Diff. Geom. , vol.35 , pp. 21-84
    • Escobar, J.1
  • 25
    • 0002416517 scopus 로고
    • Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature
    • _, Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature, Annals of Math., 136 (1992), 1-50; Addendum in Annals of Math., 139 (1994), 749-750, MR 95h:53053, Zbl 766.53033, Zbl 861.53036.
    • (1992) Annals of Math. , vol.136 , pp. 1-50
  • 26
    • 85037260590 scopus 로고
    • MR 95h:53053, Zbl 766.53033, Zbl 861.53036
    • _, Conformal deformation of a Riemannian metric to a scalar flat metric with constant mean curvature, Annals of Math., 136 (1992), 1-50; Addendum in Annals of Math., 139 (1994), 749-750, MR 95h:53053, Zbl 766.53033, Zbl 861.53036.
    • (1994) Addendum in Annals of Math. , vol.139 , pp. 749-750
  • 29
    • 0000106773 scopus 로고
    • Conformally invariant operators of standard type
    • MR 90k:58254, Zbl 683.53063
    • A.R. Gover, Conformally invariant operators of standard type, Quart. J. Math., 40 (1989), 197-207, MR 90k:58254, Zbl 683.53063.
    • (1989) Quart. J. Math. , vol.40 , pp. 197-207
    • Gover, A.R.1
  • 30
    • 85037265483 scopus 로고    scopus 로고
    • Invariants and calculus for conformal geometry
    • to appear in
    • _, Invariants and calculus for conformal geometry, to appear in Advances in Mathematics.
    • Advances in Mathematics
  • 31
    • 0001817236 scopus 로고    scopus 로고
    • Aspects of parabolic invariant theory
    • MR 2001a:58047
    • _, Aspects of parabolic invariant theory, Supp. Rend. Circ. Matem. Palermo, Ser. II, Suppl., 59 (1999), 25-47, MR 2001a:58047.
    • (1999) Supp. Rend. Circ. Matem. Palermo, Ser. Ii, Suppl. , vol.59 , pp. 25-47
  • 32
    • 84962999126 scopus 로고
    • Conformally invariant powers of the Laplacian, I: Existence
    • MR 94c:58226, Zbl 788.53011
    • C.R. Graham, R. Jenne, L. Mason and G. Sparling, Conformally invariant powers of the Laplacian, I: Existence, J. Lond. Math. Soc., 46 (1992), 557-565, MR 94c:58226, Zbl 788.53011.
    • (1992) J. Lond. Math. Soc. , vol.46 , pp. 557-565
    • Graham, C.R.1    Jenne, R.2    Mason, L.3    Sparling, G.4
  • 34
    • 0003744659 scopus 로고
    • American Mathematical Society, Providence, MR 96h:43009, Zbl 809.53057
    • S. Helgason, Geometric Analysis on Symmetric Spaces, American Mathematical Society, Providence, 1994, MR 96h:43009, Zbl 809.53057.
    • (1994) Geometric Analysis on Symmetric Spaces
    • Helgason, S.1
  • 36
    • 84990623569 scopus 로고
    • Relaxation of a variational method for impedance computed tomography
    • MR 89h:35339, Zbl 659.49009
    • R. Kohn and M. Vogelius, Relaxation of a variational method for impedance computed tomography, Comm. Pure Appl. Math., 40 (1987), 745-777, MR 89h:35339, Zbl 659.49009.
    • (1987) Comm. Pure Appl. Math. , vol.40 , pp. 745-777
    • Kohn, R.1    Vogelius, M.2
  • 39
    • 0001339558 scopus 로고
    • On the positivity of the effective action in a theory of random surfaces
    • MR 84j:58043, Zbl 506.47031
    • E. Onofri, On the positivity of the effective action in a theory of random surfaces, Commun. Math. Phys., 86 (1982), 321-326, MR 84j:58043, Zbl 506.47031.
    • (1982) Commun. Math. Phys. , vol.86 , pp. 321-326
    • Onofri, E.1
  • 40
    • 0000193161 scopus 로고
    • Extremals of determinants of Laplacians
    • MR 90d:58159, Zbl 653.53022
    • B. Osgood, R. Phillips and P. Sarnak, Extremals of determinants of Laplacians, J. Funct. Anal., 80 (1988), 148-211, MR 90d:58159, Zbl 653.53022.
    • (1988) J. Funct. Anal. , vol.80 , pp. 148-211
    • Osgood, B.1    Phillips, R.2    Sarnak, P.3
  • 41
    • 45449124033 scopus 로고
    • Compact isospectral sets of surfaces
    • MR 90d:58160, Zbl 653.53021
    • _, Compact isospectral sets of surfaces, J. Funct. Anal., 80 (1988), 212-234, MR 90d:58160, Zbl 653.53021.
    • (1988) J. Funct. Anal. , vol.80 , pp. 212-234
  • 43
    • 0003981185 scopus 로고
    • Cambridge University Press, MR 86h:83002, Zbl 538.53024
    • R. Penrose and W. Rindler, Spinors and Space-time, I, Cambridge University Press, 1984, MR 86h:83002, Zbl 538.53024.
    • (1984) Spinors and Space-time , vol.1
    • Penrose, R.1    Rindler, W.2
  • 44
    • 0034259976 scopus 로고    scopus 로고
    • Conformally covariant pseudo-differential operators
    • CMP 1 783 963
    • L. Peterson, Conformally covariant pseudo-differential operators, Diff. Geom. Appl., 13(2) (2000), 197-211, CMP 1 783 963.
    • (2000) Diff. Geom. Appl. , vol.13 , Issue.2 , pp. 197-211
    • Peterson, L.1
  • 45
    • 33744769203 scopus 로고
    • A non-local action for the trace anomaly
    • MR85g:81160
    • R. Riegert, A non-local action for the trace anomaly, Phys. Lett., 134B (1984), 56-60, MR85g:81160.
    • (1984) Phys. Lett. , vol.134 B , pp. 56-60
    • Riegert, R.1
  • 46
    • 26344438552 scopus 로고
    • Invariant operators on conformal manifolds
    • University of Vienna, archived at
    • J. Slovák, Invariant operators on conformal manifolds, Lecture Notes, University of Vienna, 1992, archived at file://ftp.math.muni.cz.
    • (1992) Lecture Notes
    • Slovák, J.1
  • 47
    • 84990627147 scopus 로고
    • Inverse boundary value problems at the boundary - Continuous dependence
    • MR 891:35213, Zbl 632.35074
    • J. Sylvester and G. Uhlmann, Inverse boundary value problems at the boundary - continuous dependence, Comm. Pure Appl. Math., 41 (1988), 197-219, MR 891:35213, Zbl 632.35074.
    • (1988) Comm. Pure Appl. Math. , vol.41 , pp. 197-219
    • Sylvester, J.1    Uhlmann, G.2
  • 48
    • 84985378927 scopus 로고
    • On conformally invariant differential operators
    • MR 88a:5820, Zbl 619.53008
    • V. Wünsch, On conformally invariant differential operators, Math. Nachr., 129 (1986), 269-281, MR 88a:5820, Zbl 619.53008.
    • (1986) Math. Nachr. , vol.129 , pp. 269-281
    • Wünsch, V.1


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