IJPAM: Volume 81, No. 2 (2012)

THE NÖRLUND ORLICZ SPACE OF
DOUBLE ENTIRE RATE SEQUENCES

N. Subramanian$^1$, P. Thirunavukarasu$^2$, P. Anbalagan$^3$
$^1$Department of Mathematics
SASTRA University
Thanjavur, 613 401, INDIA
$^2$PG & Research Department of Mathematics
Periyar E.V.R. College
Trichy, 620 023, Tamil Nadu, INDIA
$^3$Department of Mathematics
Government Arts College
Trichy, 620 022, Tamil Nadu, INDIA


Abstract. Let $\Gamma_\pi^2 $ denote the space of all double entire rate sequences. Let $\Lambda_\pi^2 $ denote the space of all double analytic rate sequences. This paper is devoted to a study of the general properties of Nörlund double Orlicz space $\eta \left({\Gamma_{f\pi}^2} \right)$ of entire rate sequences and Nörlund double Orlicz space $\eta \left({\Lambda_{f\pi}^2} \right)$ of analytic rate sequences.

Received: September 5, 2012

AMS Subject Classification: 46A45, 40G05, 46A08

Key Words and Phrases: analytic sequence, double sequence, Nörlund space, Orlicz space and entire sequence and Rate sequences

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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2012
Volume: 81
Issue: 2