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A partial solution of the Pompeiu problem. (English) Zbl 0329.35045

##### MSC:
 35N05 Overdetermined systems of PDEs with constant coefficients 35R30 Inverse problems for PDEs 35J25 Boundary value problems for second-order elliptic equations
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##### References:
 [1] Brown, L., Schreiber, B., Taylor, B. A.: Spectral synthesis and the Pompeiu problem. Ann. Inst. Fourier, Grenoble,23, 125-154 (1973) · Zbl 0265.46044 [2] Courant, R., Hilbert, D.: Methods of mathematical physics. Vol. I. New York: Interscience 1953 · Zbl 0051.28802 [3] Hörmander, L.: Linear partial differential operators. Berlin, Heidelberg, New York: Springer 1969 · Zbl 0175.39201 [4] Gunning, R., Rossi, H.: Analytic functions of several complex variables. Englewood Cliffs, N. J.: Prentice-Hall 1965 · Zbl 0141.08601 [5] Trèves, F.: Linear partial differential equations with constant coefficients. New York: Gordon and Breach 1966 · Zbl 0164.40602 [6] Dunford, N., Schwartz, J.: Linear operators. Vol. II. New York: Interscience 1963 · Zbl 0128.34803 [7] Morrey, C. B., Jr.: On the analyticity of the solutions of analytic non-linear elliptic systems of partial differential equations. Part I. Amer. J. of Math.80, 198-218 (1958) · Zbl 0081.09402 · doi:10.2307/2372830 [8] Spanier, E.: Algebraic topology. New York: McGraw-Hill 1966 · Zbl 0145.43303 [9] Courant, R., Hilbert, D.: Methods of mathematical physics. Vol. II. New York: Interscience 1962 · Zbl 0099.29504 [10] Serrin, J.: A symmetry problem in potential theory. Arch. Rat. Mech. Anal.43, 304-318 (1971) · Zbl 0222.31007 · doi:10.1007/BF00250468
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