Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



The multidimensional $p$-adic Green function

Authors: Nguyen Minh Chuong and Nguyen Van Co
Journal: Proc. Amer. Math. Soc. 127 (1999), 685-694
MSC (1991): Primary 11S80; Secondary 81T99
MathSciNet review: 1618721
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A proof much simpler than the one given by Bikulov (Investigation of the $p$-adic Green function, Teoret. Mat. Fiz. 87 (1991), 376-390) for properties of the 2-dimensional $p$-adic Green function is shown. By this method one can treat a multidimensional case, and some sharp estimates are obtained.

References [Enhancements On Off] (What's this?)

  • 1. A. Kh. Bikulov, Investigation of a 𝑝-adic Green function, Teoret. Mat. Fiz. 87 (1991), no. 3, 376–390 (Russian, with English summary); English transl., Theoret. and Math. Phys. 87 (1991), no. 3, 600–610. MR 1129672,
  • 2. Nguyen Minh Chuong, Nguyen Van Co and Tran Quoc Binh, $p$-adic distributions and Sobolev spaces, Preprint 96/10, Hanoi Institute of Mathematics.
  • 3. Nguyen Minh Chuong and Nguyen Van Co, A new proof for $p$-adic Green function, Preprint 1997, Hanoi Institute of Mathematics.
  • 4. Nguyen Minh Chuong, Nguyen Minh Tri and Le Quang Trung, Theory of Partial Differential Equations, Sci. & Jechn. Publ. House, Hanoi (1995).
  • 5. G. Christol and B. Dwork, Effective 𝑝-adic bounds at regular singular points, Duke Math. J. 62 (1991), no. 3, 689–720. MR 1104814,
  • 6. Andrei Khrennikov, 𝑝-adic valued distributions in mathematical physics, Mathematics and its Applications, vol. 309, Kluwer Academic Publishers Group, Dordrecht, 1994. MR 1325924
  • 7. Neal Koblitz, 𝑝-adic numbers, 𝑝-adic analysis, and zeta-functions, 2nd ed., Graduate Texts in Mathematics, vol. 58, Springer-Verlag, New York, 1984. MR 754003
  • 8. V. S. Vladimirov, I. V. Volovich, and E. I. Zelenov, 𝑝-\cyr adicheskiĭ analiz i matematicheskaya fizika, VO “Nauka”, Moscow, 1994 (Russian, with Russian summary). MR 1349578

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 11S80, 81T99

Retrieve articles in all journals with MSC (1991): 11S80, 81T99

Additional Information

Nguyen Minh Chuong
Affiliation: Hanoi Institute of Mathematics, P.O. Box 631 Boho, 10 000 Hanoi, Vietnam

Nguyen Van Co
Affiliation: Department Of Mathematics, Hanoi State University, Mai Dich, Tu Liem, Hanoi, Vietnam

Received by editor(s): July 1, 1997
Additional Notes: This paper was supported by the National Natural Science Foundation of Vietnam
Communicated by: Dennis A. Hejhal
Article copyright: © Copyright 1999 American Mathematical Society