A Tauberian theorem for the generalized Norlund summability method
Küçük Resim Yok
Tarih
2020
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Walter De Gruyter Gmbh
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
Let (p(n)) and (q(n)) be any two non-negative real sequences, with R-n := Sigma(n)(k=0) p(k)q(n-k) not equal 0 (n epsilon N). Let Sigma(infinity)(k=0) ak be a series of real or complex numbers with partial sums (s(n)), and set t(n)(p,q) := 1/R-n Sigma(n)(k=0) p(k)q(n-k)s(k) for n epsilon N. in this paper, we present the necessary and sufficient conditions under which the existence of the limit lim(n ->infinity) s(n) = L follows from that of lim(n ->infinity) t(n)(p, q) = L. These conditions are one-sided or two-sided if (sn) is a sequence of real or complex numbers, respectively.
Açıklama
Anahtar Kelimeler
Generalized Norlund summability, one-sided and two-sided Tauberian conditions
Kaynak
Georgian Mathematical Journal
WoS Q Değeri
Q4
Scopus Q Değeri
Cilt
27
Sayı
1
