Cauchy multiplication of Euler summable series in ultrametric fields

• Autorzy: Deepa R. , Natarajan P. N. , Srinivasan V.
• Języki publikacji: EN

Abstrakty

EN

Euler summability method in a complete, non-trivially valued, ultrametric field of the characteristic zero was introduced by Natarajan in [7]. Some properties of the Euler summability method in such fields were studied in [2] and [7]. The purpose of the present note is to continue the study and to prove a pair of theorems on the Cauchy product of Euler summable sequences and series.

Słowa kluczowe

EN

ultrametric field; regular method; euler summability method; Cauchy product

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2013
• Tom: Vol 53, No. 1
• Strony: 73--79
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Deepa R.

• Department of Mathematics, Faculty of Engineering and Technology, SRM Universit Kattankulathur 603 203, India

autor

Natarajan P. N.

• Old No. 2/3, New No. 3/3, Second Main Road, R.A. Puram, Chennai 600 028, India

autor

Srinivasan V.

• Department of Mathematics, Faculty of Engineering and Technology, SRM University Kattankulathur 603 203, India

Bibliografia

• [1] G. Bachman, Introduction to p-adic numbers and valuation theory, Academic Press, 1964.
• [2] R. Deepa, P.N. Natarajan and V. Srinivasan, Some properties of the Euler summability method in complete ultrametric fields (submitted for publication).
• [3] G.H. Hardy, Divergent Series, Oxford University Press, 1949.
• [4] A.F. Monna, Sur le théorème de Banach-Steinhaus, Indag. Math. 25 (1963), 121–131.
• [5] P.N. Natarajan, Multiplication of series with terms in a non-archimedean field, Simon Stevin 52 (1978), 157-160.
• [6] P.N. Natarajan, Criterion for regular matrices in non-archimedean fields, J. Ramanujan Math. Soc. 6 (1991), 185–195.
• [7] P.N. Natarajan, Euler and Taylor methods of summability in complete ultrametric fields, J. Analysis 11 (2003), 33–41.
• [8] R.E. Powell and S.M. Shah, Summability theory and applications, Prentice-Hall of India, 1988.