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Branch points, Fourier integrals and Pompeiu problem

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Si prova che sep è un polinomio e la mappa\(h(w) = \sqrt {p(w)} \) è univalente sul disco unitarioD del piano complesso, allora Ω=h(D) ha la proprietà di Pompeiu.

Abstract

Leth be the square root of a polynomial and assume thath is univalent on the unitary disk of the complex plane. Then the set Ω=h(D) has the Pompeiu property.

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References

  1. L. Brown—B. M. Schreiber—B. A. Taylor Spectral synthesis and the Pompeiu problem, Ann. Inst. Fourier,23 (1973), pp. 125–154.

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  2. N. Garofalo—F. Segala Univalent functions and Pompeiu problem, Trans. Amer. Math. Soc.,346 (1) (1994), pp. 137–146.

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Author notes

  1. Fausto Segala

    Present address: Università di Ferrara, Italy

  2. Matteo Triossi

    Present address: Universidad Carlos III, Getafe, Spain

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    1. Fausto Segala
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    2. Matteo Triossi
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    Segala, F., Triossi, M. Branch points, Fourier integrals and Pompeiu problem. Ann. Univ. Ferrara 47, 169–175 (2001). https://doi.org/10.1007/BF02838181

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