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Pseudodifferential operators on adele rings and wavelet bases

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References

  1. S. Albeverio, A. Yu. Khrennikov, and V. M. Shelkovich, Theory of p-Adic Distributions: Linear and Nonlinear Models (Cambridge Univ. Press, Cambridge, 2010).

    Book  MATH  Google Scholar 

  2. I. Aref’eva, B. Dragovic, and I. Volovich, Phys. Lett. A. 209(4), 445–450 (1998).

    MathSciNet  Google Scholar 

  3. Yu. M. Berezanskii, Self-Adjoint Operators in Spaces of Functions of Infinitely Many Variables (Naukova Dumka, Kiev, 1978; Am. Math. Soc., Providence, R.I., 1986).

    Google Scholar 

  4. I. M. Gel’fand, M. I. Graev, and I. I. Pyatetskii-Shapiro, Generalized Functions, Vol. 6: Representation Theory and Automorphic Functions (Nauka, Moscow, 1959; Academic, Boston, 1990).

    Google Scholar 

  5. A. Yu. Khrennikov, V. M. Shelkovich, and M. Skopina, p-Adic Numbers Ultrametric Anal. Appl. 1(2), 145–156 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. V. Kosyak, A. Yu. Khrennikov, and V. M. Shelkovich, Dokl. Math. 85, 75–79 (2012).

    Article  MATH  Google Scholar 

  7. A. Yu. Khrennikov, A. V. Kosyak, and V. M. Shelkovich, Wavelet Analysis on Adeles and Pseudo-Differential Operators, arXiv.math: FA/1107.1700v1, 2011.

  8. S. V. Kozyrev, Izv. Akad. Nauk, Ser. Mat. 66(2), 149–158 (2002).

    MathSciNet  Google Scholar 

  9. Yu. A. Neretin, On Adelic Model of Boson Fock Space (Am. Math. Soc., Providence, R.I., 2007), Ser. 2, 221, 193–202.

    Google Scholar 

  10. J. von Neumann, Compos. Math. 15(1), 1–77 (1939).

    Google Scholar 

  11. V. M. Shelkovich and M. Skopina, J. Fourier Anal. Appl. 15(4), 366–393 (2009).

    Article  MathSciNet  MATH  Google Scholar 

  12. S. G. Samko, A. A. Kilbas, and O. I. Marichev, Integrals and Derivatives of Fractional Order and Some of Their Applications (Nauka i Tekhnika, Minsk, 1987) [in Russian].

    MATH  Google Scholar 

  13. V. M. Shelkovich, Izv. Akad. Nauk, Ser. Mat. 75(6), 163–194 (2011).

    MathSciNet  Google Scholar 

  14. V. S. Vladimirov, Izv. Akad. Nauk, Ser. Mat. 60(1), 63–86 (1996).

    Google Scholar 

  15. V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, p-Adic Analysis and Mathematical Physics (Nauka, Moscow, 1994) [in Russian].

    Google Scholar 

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Authors and Affiliations

  1. Institute of Mathematics, National Academy of Sciences of Ukraine, Tereshchenkovskaya ul. 3, Kiev, 01601, Ukraine

    A. V. Kosyak

  2. International Center for Mathematical Modeling in Physics and Cognitive Sciences MSI, Linnaeus University, Vaxjo-Kalmar, SE-351 95, Vaxjo, Sweden

    A. Yu. Khrennikov

  3. St. Petersburg State Architecture and Civil Engineering University, Vtoraya Krasnoarmeiskaya ul. 4, St. Petersburg, 190005, Russia

    V. M. Shelkovich

Authors
  1. A. V. Kosyak
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  2. A. Yu. Khrennikov
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  3. V. M. Shelkovich
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Correspondence to A. V. Kosyak.

Additional information

Original Russian Text © A.V. Kosyak, A.Yu. Khrennikov, V.M. Shelkovich, 2012, published in Doklady Akademii Nauk, 2012, Vol. 444, No. 3, pp. 253–257.

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Kosyak, A.V., Khrennikov, A.Y. & Shelkovich, V.M. Pseudodifferential operators on adele rings and wavelet bases. Dokl. Math. 85, 358–362 (2012). https://doi.org/10.1134/S1064562412030167

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  • DOI: https://doi.org/10.1134/S1064562412030167

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