Propagation of singularities from singular and infinite points in certain complex-analytic Cauchy problems and an application to the Pompeiu problem
Peter Ebenfelt
Source: Duke Math. J. Volume 73, Number 3
(1994), 561-582.
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077289016
Mathematical Reviews number (MathSciNet): MR1262927
Zentralblatt MATH identifier: 0833.35004
Digital Object Identifier: doi:10.1215/S0012-7094-94-07323-7
References
[Be] C. A. Berenstein, An inverse spectral theorem and its relation to the Pompeiu problem, J. Analyse Math. 37 (1980), 128–144.
Mathematical Reviews (MathSciNet): MR82b:35031
Zentralblatt MATH: 0449.35024
Digital Object Identifier: doi:10.1007/BF02797683
[BY] C. A. Berenstein and P. C. Yang, An inverse Neumann problem, J. Reine Angew. Math. 382 (1987), 1–21.
Mathematical Reviews (MathSciNet): MR88k:31007
Zentralblatt MATH: 0623.35078
[Bj] J.-E. Björk, Rings of Differential Operators, North-Holland Math. Library, vol. 21, North-Holland, Amsterdam, 1979.
Mathematical Reviews (MathSciNet): MR82g:32013
Zentralblatt MATH: 0499.13009
[BK] E. Brieskorn and H. Knörrer, Plane Algebraic Curves, Birkhäuser, Basel, 1986.
Mathematical Reviews (MathSciNet): MR88a:14001
Zentralblatt MATH: 0588.14019
[CL] E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, 1955.
Mathematical Reviews (MathSciNet): MR16,1022b
Zentralblatt MATH: 0064.33002
[D] P. J. Davis, The Schwarz Function and its Applications, Carus Math. Monographs, vol. 17, Math. Assoc. America, Buffalo, 1974.
Mathematical Reviews (MathSciNet): MR53:11031
Zentralblatt MATH: 0293.30001
[E1] P. Ebenfelt, Some results on the Pompeiu problem, Ann. Acad. ci. Fenn. Ser. AI. 18 (1993), no. 2, 323–341.
Mathematical Reviews (MathSciNet): MR95b:30061
Zentralblatt MATH: 0793.30034
[E2] P. Ebenfelt, Singularities of the solution to a certain Cauchy problem and an application to the Pompeiu problem, Duke Math. J. 71 (1993), no. 1, 119–142.
Mathematical Reviews (MathSciNet): MR94k:35006
Zentralblatt MATH: 0797.35129
Digital Object Identifier: doi:10.1215/S0012-7094-93-07106-2
Project Euclid: euclid.dmj/1077289839
[GS] N. Garofalo and F. Segala, New results on the Pompeiu problem, Trans. Amer. Math. Soc. 325 (1991), no. 1, 273–286.
Mathematical Reviews (MathSciNet): MR91h:35322
Zentralblatt MATH: 0737.35147
Digital Object Identifier: doi:10.2307/2001671
JSTOR: links.jstor.org
[GH] P. Griffiths and J. Harris, Principles of Algebraic Geometry, Pure Appl. Math., Wiley, New York, 1978.
Mathematical Reviews (MathSciNet): MR80b:14001
Zentralblatt MATH: 0408.14001
[Ha] J. Hadamard, Lectures on Cauchy's Problem in Linear Partial Differential Equations, Dover Publications, New York, 1952.
Mathematical Reviews (MathSciNet): MR14,474f
Zentralblatt MATH: 0049.34805
[He] P. Henrici, A survey of I. N. Vekua's theory of elliptic partial differential equations with analytic coefficients, Z. Angew. Math. Phys. 8 (1957), 169–203.
Mathematical Reviews (MathSciNet): MR19,38a
Zentralblatt MATH: 0078.27802
Digital Object Identifier: doi:10.1007/BF01600500
[K] D. Khavinson, Singularities of harmonic functions in $\mathbbC^n$, Several Complex Variables and Complex Geometry, Part 3 (Santa Cruz, CA, 1989), Proc. Sympos. Pure Math., vol. 52, Amer. Math. Soc., Providence, 1991, pp. 207–217.
Mathematical Reviews (MathSciNet): MR92m:35009
Zentralblatt MATH: 0755.31003
[L] J. Leray, Problème de Cauchy. I. Uniformisation de la solution du problème linéaire analytique de Cauchy près de la variété qui porte les données de Cauchy, Bull. Soc. Math. France 85 (1957), 389–429.
Mathematical Reviews (MathSciNet): MR21:2102
Zentralblatt MATH: 0108.09501
[M] B. Malgrange, Équations Differentielles à Coefficients Polynomiaux, Progr. Math., vol. 96, Birkhäuser, Boston, 1991.
Mathematical Reviews (MathSciNet): MR92k:32020
Zentralblatt MATH: 0764.32001
[O] F. W. J. Olver, Bessel functions of integer order, Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables eds. M. Abramowitz and I. A. Stegun, National Bureau of Standards Applied Mathematics Series, vol. 55, Wiley-Interscience, New York, 1972, pp. 355–434.
[S] H. S. Shapiro, The Schwarz Function and its Generalization to Higher Dimensions, Univ. Arkansas Lecture Notes Math Sci., vol. 9, Wiley, New York, 1992.
Mathematical Reviews (MathSciNet): MR93g:30059
Zentralblatt MATH: 0784.30036
[W1] S. A. Williams, A partial solution of the Pompeiu problem, Math. Ann. 223 (1976), no. 2, 183–190.
Mathematical Reviews (MathSciNet): MR54:2996
Zentralblatt MATH: 0329.35045
Digital Object Identifier: doi:10.1007/BF01360881
[W2] S. A. Williams, Analyticity of the boundary for Lipschitz domains without the Pompeiu property, Indiana Univ. Math. J. 30 (1981), no. 3, 357–369.
Mathematical Reviews (MathSciNet): MR82j:31009
Zentralblatt MATH: 0439.35046
Digital Object Identifier: doi:10.1512/iumj.1981.30.30028
[Z] L. Zalcman, A bibliographic survey of the Pompeiu problem, Approximation by Solutions of Partial Differential Equations (Hanstholm, 1991) eds. M. Goldstein and W. Haussman, NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 365, Kluwer, Dordrecht, 1992, pp. 185–194.
Mathematical Reviews (MathSciNet): MR93e:26001
Zentralblatt MATH: 0830.26005
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