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The duality principle and inversion of Laplace–Stielties transforms

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Abstract

The fundamental relation between the Laplace transform, the Stielties transform, and the generalized integral equation of refraction is revealed, and a duality principle is formulated for the solution of inverse problems of radio physics. New formulas of the Laplace-transform inversion satisfying the duality principle are obtained. There is no necessity of contour integration in a complex plane for the relations found, which considerably simplifies the reconstruction of originals and makes it possible to control systematic errors in the experimental data.

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References

  1. M. I. Kontorovich, Operational Calculus and Processes in Electronic Circuits (Sov. radio, Moscow, 1975) [in Russian].

    Google Scholar 

  2. A. G. Pavelyev and D. A. Pavel’ev, Preprint No. 10(561) (IRE AN USSR, 1991) [in Russian].

    Google Scholar 

  3. A. G. Pavelyev, Dokl. Akad. Nauk 311 (3), 603 (1990).

    MathSciNet  Google Scholar 

  4. G. Cerofolini, G. Ferla, and G. Spadini, Thin Solid Films 68, 315 (1980).

    Article  ADS  Google Scholar 

  5. N. A. Armand, V. A. Andrianov, and V. M. Smirnov, Radiotekh. Elektron. (Moscow) 32 (4), 673 (1987).

    ADS  Google Scholar 

  6. A. G. Pavelyev, Izv. Vyssh. Uchebn. Zaved. Mat. No. 9, 45 (1990).

    Google Scholar 

  7. A. G. Pavelyev, Zh. Vychsl. Mat. Fiz. 27 (7), 963 (1987).

    Google Scholar 

  8. A. Gurvits and R. Kurant, Theory of Functions (Nauka, Moscow, 1968) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Kotelnikov Institute of Radio Engineering and Electronics, Russian Academy of Sciences (Fryazino Branch), Fryazino, Moscow oblast, 141120, Russia

    A. G. Pavelyev

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  1. A. G. Pavelyev
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Correspondence to A. G. Pavelyev.

Additional information

Original Russian Text © A.G. Pavelyev, 2016, published in Doklady Akademii Nauk, 2016, Vol. 467, No. 6, pp. 656–659.

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Pavelyev, A.G. The duality principle and inversion of Laplace–Stielties transforms. Dokl. Phys. 61, 175–178 (2016). https://doi.org/10.1134/S1028335816040121

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  • DOI: https://doi.org/10.1134/S1028335816040121

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