64
Views
0
CrossRef citations to date
0
Altmetric
Original Articles

Operational calculus on the ring of p-adic integers

Pages 327-335 | Received 01 Mar 2010, Published online: 17 May 2011

References

  • Berg , L. 1962 . Eihführrung in Die Operatorenrechnung Berlin D-tsch. Verl. Wiss (in German)
  • Brand , L. 1964 . A division algebra for sequences and its associated operational calculus . Amer. Math. Monthly , 17 ( 7 ) : 719 – 728 .
  • Brychkov , Yu. A. , Prudnikov , A. P. and Shishov , V. S. 1979 . “ Operational calculus ” . In Itogi Nauki i Tekhniki. Mathematical Analysis Vol. 16 , 99 – 148 . Moscow VINITI Akad. Nauk SSSR (in Russian)
  • Colombeau , J.-F. 1985 . Elementary Introduction to New Generalized Functions , Amsterdam : North Holland .
  • Mahler , K. 1973 . Introduction to p-adic Numbers and their Functions , Cambridge : Cambridge University Press .
  • Mikusiński , J. and Boehme , Th. K. 1987 . Operational Calculus , Vol. II , New York : PWN & Pergamon .
  • Radyno , Ya. V. 1999 . “ Extensions of algebras, mnemofunctions and their applications ” . In Nonlinear Theory of Generalized Functions , Edited by: Oberguggenberger , M. , Grosser , M. , Kunzinger , M. and Hormann , G. 209 – 218 . Boca Raton : Chapman&Hall/CRC .
  • Richalet , J. 1965 . Operational calculus for finite rings . IEEE Trans. Circuit Theory , 12 ( 4 ) : 558 – 570 .
  • Schikhof , W. H. 1984 . Ultrametric Calculus. An Introduction to p-adic Analysis , Cambridge : Cambridge University Press .
  • Struble , R. A. 1977 . Analytical and algebraic aspects of the operational calculus . SIAM Rev. , 19 ( 3 ) : 403 – 436 .
  • Todorov , T. D. 2005 . Existence and uniqueness of v-asymptotic expansions and Colombeau's generalized numbers . J. Math. Anal. Appl. , 312 ( 1 ) : 261 – 279 . Available at arXiv:math/0601720v1 [math.CA]
  • Vasilach , S. 1970 . Sur un extension des opérateurs paraboliques en calcul opérationnel des distributions à support dans , n≥1 . C. R. Math. Acad. Sci. Paris , 270 : 931 – 934 .
  • Vladimirov , V. S. , Volovich , I. V. and Zelenov , E. I. 1994 . p-Adic Analysis and Mathematical Physics , Singapore : World Scientific .
  • Yosida , K. 1984 . Operational Calculus , New York : Springer-Verlag .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.