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On the Inversion of the Local Pompeiu Transformation

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Ukrainian Mathematical Journal Aims and scope

Abstract

The inversion of the local Pompeiu transform for a triangle is constructed.

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REFERENCES

  1. K. A. Berenstein and D. Struppa, “Complex analysis and convolution equations,” in: VINITI Series in Contemporary Problems in Mathematics, Fundamental Trends [in Russian], Vol. 54, VINITI, Moscow (1989), pp. 5–111.

    Google Scholar 

  2. L. Zalcman, “A bibliographic survey of the Pompeiu problem,” in: B. Fuglede et al. (editors), Approximation by Solutions of Partial Differential Equations(1992), pp. 185–194.

  3. V. V. Volchkov, “Ultimate version of the local theorem on two radii,” Mat. Sb., 186, No. 6, 15–34 (1995).

    Google Scholar 

  4. V. V. Volchkov, “On the sets of injectivity of the Pompeiu transformation,” Mat. Sb., 190, No. 11, 51–66 (1999).

    Google Scholar 

  5. V. V. Volchkov, “Extremal problems on Pompeiu sets,” Mat. Sb., 191, No. 5, 4–16(2000).

    Google Scholar 

  6. C. A. Berenstein and R. Gay, “Le probleme de Pompeiu locale,” J. Anal. Math., 52, 133–166(1989).

    Google Scholar 

  7. C. A. Berenstein, R. Gay, and A. Yger, “Inversion of the Pompeiu transform,” J. Anal. Math., 54, 259–287 (1990).

    Google Scholar 

  8. V. V. Volchkov, “On one extremal problem related to the Morera theorem,” Mat. Zametki, 60, No. 6, 804–809 (1996).

    Google Scholar 

  9. V. V. Volchkov, “Extremal versions of the Pompeiu problem,”Mat. Zametki, 59, No. 5, 671–680 (1996).

    Google Scholar 

  10. P. A. Masharov, “Extremal problems on sets with local Pompeiu property,” Dopov. Akad. Nauk Ukr., No. 7, 126–132 (2001).

    Google Scholar 

  11. V. S. Vladimirov, Equations of Mathematical Physics [in Russian], Nauka, Moscow (1981).

  12. L. Hörmander, The Analysis of Linear Differential Operators. IV. Fourier Integral Operators, Springer, Berlin (1985).

  13. É. Ya. Riekstyn'sh,Asymptotic Decompositions of Integrals[in Russian], Vol. 1, Zinatne, Riga (1974).

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Authors and Affiliations

  1. Donetsk University, Donetsk

    N. P. Volchkova

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  1. N. P. Volchkova
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Volchkova, N.P. On the Inversion of the Local Pompeiu Transformation. Ukrainian Mathematical Journal 55, 1054–1060 (2003). https://doi.org/10.1023/B:UKMA.0000010604.68266.ee

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  • DOI: https://doi.org/10.1023/B:UKMA.0000010604.68266.ee

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