ON BOUNDEDNESS WITH SPEED λ IN ULTRAMETRIC FIELDS

Natarajan Narayanasubramanian Pinnangudi

DOI Number
https://doi.org/10.22190/FUMI211031045P
First page
643
Last page
649

Abstract


In the present paper, K denotes a complete, non-trivially valued, ultrametric (or non-archimedean) field. Entries of sequences, infinite series and infinite matrices are in K. Following Kangro [2, 3, 4], we introduce the concept of boundedness with speed λ or λ-boundedness. We then obtain a characterization of the matrix class (mλ , mµ ), where mλ denotes the set of all λ-bounded sequences in K. We conclude the paper with a remark about the matrix class (c λ , mµ ), where c λ denotes the set of all λ-convergent sequences in K.

Keywords

Ultrametic (or non-archimedean) field, boundedness with speed $\lambda$ (or $\lambda$-boundedness), $\lambda$-bounded by the matrix $A$ or $A^\lambda$-bounded, matrix class $(m^\lambda, m^\mu)$, matrix class $(c^\lambda, m^\mu)$

Full Text:

PDF

References


Ants Aasma, Hemen Dutta and P.N. Natarajan, An Introductory Course in Summability Theory, Wiley, 2017.

G. Kangro, On the summability factors of the Bohr-Hardy type for a

given speed I, Eesti NSV Tead. Akad. Toimetised F¨u¨us. - Mat., 18 (2)

(1969), 137–146.

G. Kangro, On the summability factors of the Bohr-Hardy type for a

given speed II, Eesti NSV Tead. Akad. Toimetised F¨u¨us. - Mat., 18 (4)

(1969), 387–395.

G. Kangro, Summability factors for the series λ-bounded by the methods of Riesz and Ces`aro, Tartu Riikl. Ul. Toimetised, 277 (1971), 136–154.

P.N. Natarajan, The Steinhaus theorem for Toeplitz matrices in nonarchimedean fields, Comment. Math. Prace Mat., 20 (1978), 417–422.

P.N. Natarajan, An Introduction to Ultrametric Summability Theory, Springer, 2014.

P.N. Natarajan, On covergence and summability with speed in

ultrametric fields (Communicated for publication).

V.K. Srinivasan, On certain summation processes in the p-adic field, Indag. Math., 27 (1965), 319–325.




DOI: https://doi.org/10.22190/FUMI211031045P

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)