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Siberian Mathematical Journal

, Volume 13, Issue 3, pp 453–456 | Cite as

The radial indicator in the theory of Borel summability with some applications

  • V. M. Trutnev
Article

Keywords

Borel Summability Radial Indicator 
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Literature Cited

  1. 1.
    V. K. Ivanov, “The growth characteristics of entire functions of two variables with applications to the summability of double series,” Matem. Sb.,46 (89), No. 1, 131–140 (1959).Google Scholar
  2. 2.
    L. A. Aizenberg and V. M. Trutnev, A Borel Summation Method for n-tuple Power Series. Transactions of the All-Union Symposium on the Theory of Holomorphic Functions of Several Complex Variables [in Russian], Krasnoyarsk (1969), pp. 6–7.Google Scholar
  3. 3.
    L. A. Aizenberg and V. M. Trutnev, “A Borel summation method for n-tuple power series,” Sibirsk. Matem. Zh.,12, No. 6, 1895–1901 (1971).Google Scholar
  4. 4.
    G. H. Hardy, Divergent Series [Russian translation], IL, Moscow (1951).Google Scholar
  5. 5.
    V. Bernstein, “Sur une generalisation de la méthode de sommation exponentielle de M. Borel,” Compt. Rend. Acad. Sci.,194, 1887–1889 (1932).Google Scholar
  6. 6.
    G. Polya, “Untersuchen über Lücken und Singularitäten von Potenzreihen,” Math. Z. 19, 549–640 (1929).Google Scholar
  7. 7.
    L. Ehrenpreis, “A fundamental principle for systems of linear differential equations with constant coefficients and some of its applications,” Proc. Intern. Symp. on Linear Spaces, Jerusalem, 161–174 (1951).Google Scholar
  8. 8.
    A. Martineau, “Sur les functionelles analytiques et la transformation de Fourier-Borel,” J. Anal. Math.,9, 1–164 (1963).Google Scholar
  9. 9.
    L. Hörmander, Introduction to the Theory of Functions of Several Complex Variables [Russian translation], Mir (1968).Google Scholar
  10. 10.
    L. I. Ronkin, Introduction to the Theory of Entire Functions of Several Variables [in Russian], Fizmatgiz, Moscow (1971).Google Scholar
  11. 11.
    L. A. Aizenberg, “Linear convexity in Cn and the separation of singularities of holomorphic functions,” Bull. Acad. Pol. Sci., Ser. Sci. Math., Astron. et Phys.,15, No. 7, 487–495 (1967).Google Scholar
  12. 12.
    L. A. Aizenberg, “The expansion of holomorphic functions of several complex variables in partial fractions,” Sibirsk. Matem. Zh.,8, No. 5, 1224–1242 (1967).Google Scholar
  13. 13.
    C. O. Kiselman, “On entire functions of exponential type and indicators of analytic functionals,” Acta Math., 117, 1–35 (1967).Google Scholar

Copyright information

© Consultants Bureau 1972

Authors and Affiliations

  • V. M. Trutnev

There are no affiliations available

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