Publication Cover
Applicable Analysis
An International Journal
Volume 64, 1997 - Issue 1-2
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Original Articles

The pompeiu problem

Pages 19-26 | Received 01 Nov 1996, Published online: 02 May 2007

  • Alexandrov , A. 1962 . A characteristic property of spheres . Annali di Matematica , 58 : 303 – 315 .
  • Agranovasky , M. , Berenstein , C. , Chang , D. and Pasquas , D. 1994 . Injectivity of the Pompeiu transform in the Heisenberg group . Jour. d'Analyse Math. , 63 : 131 – 173 .
  • Bagchi , S. and Sitaram , A. 1990 . The Pompeiu problem revisited . L'Enseignement Math. , 36 : 67 – 91 .
  • Berenstein , C. 1980 . An inverse spectral problem and its relation to the Pompeiu problem . J. d'Analyse Math. , 37 : 128 – 144 .
  • Berenstein , C. and Yang , P. 1987 . An inverse Neumann problem . J. reine und angew. Math. , 382 : 1 – 21 .
  • Berenstein , C. and Zalcman , L. 1980 . Pompeiu's problem on symmetric spaces . Comm. Math. Helvet. , 55 : 593 – 621 .
  • Brown , L. , Schreiber , B. and Taylor , B.A. 1973 . Spectral synthesis and the Pompeiu problem . Ann. Inst. Fourier , 23 ( N3 ) : 125 – 154 .
  • Garofalo , N. and Segala , F. 1993 . Another step toward the solution of the Pompeiu problem . Comm. PDE , 18 ( N3 ) : 491 – 503 .
  • Kinderlehrer , D. and Nirenberg , L. 1977 . Regularity in free boundary porblems . Ann. Sc. Norm. Super. Pisa , 4 ( N3 ) : 373 – 391 .
  • Pompeiu , D. 1929 . Sur une propriete integrale des fonctions de deux variables reelles . Bull. Sci. Acad. Roy. Belgique , 5 ( 15 ) : 265 – 269 .
  • Ramm , A.G. 1992 . Multidimensional Inverse Scattering Problems , New York : Longman/Wiley . Expanded Russian edition Mir, Moscow 1994
  • Ramm , A.G. and Katsevich , A.I. 1996 . The Radon Transform and Local Tomography , CRC Press .
  • Ramm , A.GT. 1986 . “ Scattering by Obstacles ” . In Ph.D. Thesis , Edited by: Reidel , D. Dordrecht .
  • Rawat , R. and Sitaram , A. 1995 . The injectivity of the Pompeiu tranform and analogues of the Wiener tauberian teorem . Israel J. Math. , 91 : 307 – 315 .
  • Serrin , J. 1971 . A symmetry problem in potential theory . Arch. Rat. Mech. Anal. , 43 : 304 – 318 .
  • Vogelius , M. 1994 . An inverse problem for the equation Δu = -cu-d . Ann. Inst Fourier , 44 ( 4 ) : 1181 – 1209 .
  • Williams , S. 1976 . A partial solution of the Pompeiu problem . Math. Ann. , 233 ( 4 ) : 183 – 190 .
  • Williams , S. 1981 . Analytictiy of the boundary for Lipschitz domains without Pompeiu property . Indiana Univ. Math. J. , 30 ( 4 ) : 357 – 369 .
  • Zalcman , L. 1972 . Analyticity and the Pompeiu Problem . Arch. Rat. Mech. Anal. , 47 ( 4 ) : 237 – 254 .
  • Kobayashi , T. 1989 . The asymptotic behavior of the null variety of a convex domain in a non-positively curved space form . J. Fac. Sci. Univ. Tokyo , 36 ( 4 ) : 389 – 478 .
  • Kobayashi , T. 1996 . Convex domains and the Fourier transform on spaces of constant courvature , Paris : Hermann .
  • Kobayashi , T. 1993 . Perturbations of domains in the Pompeiu problem . Comm. Anal. Geom. , 1 : 515 – 541 .
  • Agranovsky , M. 1993 . On the stability of the spectrum in the Pompeiu problem . J. Math Anal. Appl. , 178 : 269 – 279 .
  • Aviles , P. 1986 . Symmetry properties related to Pompeiu's problem . Amer. J. Math , 108 : 1023 – 1036 .
  • Zalcman , L. 1992 . “ A bibliographical survey of the Pompeiu Problem ” . In Approximation by solutions of partial differential equations , Edited by: Fuglede , B. 177 – 186 . Dordrecht : Kluwer Acad. .
  • Agranovsky , M. and Semenov , A. in press . Deformation of balls in Schiffer' conjecture for Riemannian symmetric spaces .

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