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2008 | 6 | 4 | 581-594
Tytuł artykułu

Four dimensional matrix characterization of double oscillation via RH-conservative and RH-multiplicative matrices

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Języki publikacji
EN
Abstrakty
EN
In 1939 Agnew presented a series of conditions that characterized the oscillation of ordinary sequences using ordinary square conservative matrices and square multiplicative matrices. The goal of this paper is to present multidimensional analogues of Agnew’s results. To accomplish this goal we begin by presenting a notion for double oscillating sequences. Using this notion along with square RH-conservative matrices and square RH-multiplicative matrices, we will present a series of characterization of this sequence space, i.e. we will present several necessary and sufficient conditions that assure us that a square RH-multiplicative(square RH-conservative) be such that $$ P - \mathop {limsup}\limits_{(m,n) \to \infty ;(\alpha ,\beta ) \to \infty } \left| {\sigma _{m,n} - \sigma _{\alpha ,\beta } } \right| \leqslant P - \mathop {limsup}\limits_{(m,n) \to \infty ;(\alpha ,\beta ) \to \infty } \left| {s_{m,n} - s_{\alpha ,\beta } } \right| $$ for each double real bounded sequences {s k;l} where $$ \sigma _{m,n} = \sum\limits_{k,l = 1,1}^{\infty ,\infty } {a_{m,n,k,l,} s_{k,l} } . $$ In addition, other implications and variations are also presented.
Wydawca
Czasopismo
Rocznik
Tom
6
Numer
4
Strony
581-594
Opis fizyczny
Daty
wydano
2008-12-01
online
2008-10-08
Twórcy
autor
Bibliografia
  • [1] Agnew R.P., On oscillations of real sequences and of their transforms by square matrices, Amer. J. Math., 1939, 61, 683–699 http://dx.doi.org/10.2307/2371323
  • [2] Hamilton H.J., Transformations of multiple sequences, Duke Math. J., 1936, 2, 29–60 http://dx.doi.org/10.1215/S0012-7094-36-00204-1
  • [3] Pringsheim A., Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 1900, 53, 289–321 (in German) http://dx.doi.org/10.1007/BF01448977
  • [4] Robison G.M., Divergent double sequences and series, Trans. Amer. Math. Soc., 1926, 28, 50–73 http://dx.doi.org/10.2307/1989172
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-008-0043-7
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