Tauberian-Type Results for Convolution of Sequences

1987 ◽  
pp. 103-113 ◽  
Author(s):  
Dennis C. Russell
Keyword(s):  
Tauberian Type

Tauberian type theorems for double series summable by Cesaro methods

1972 ◽  
Vol 23 (6) ◽  
pp. 597-606 ◽  
Author(s):  
M. A. Kalatalova
Keyword(s):  
Double Series ◽  
Tauberian Type

Some Tauberian type theorems for ratios of functions

1971 ◽  
Vol 22 (6) ◽  
pp. 646-656
Author(s):  
I. P. Pobyvanets
Keyword(s):  
Tauberian Type

AN OSCILLATION THEOREM OF TAUBERIAN TYPE

1950 ◽  
Vol 1 (1) ◽  
pp. 243-247 ◽  
Author(s):  
N. A. BOWEN ◽  
A. J. MACINTYRE
Keyword(s):  
Oscillation Theorem ◽  
Tauberian Type

scholarly journals On the L1-convergence of Fourier transforms

1996 ◽  
Vol 60 (3) ◽  
pp. 405-420
Author(s):  
Dᾰng Vũ Giang ◽  
Ferenc Móricz
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
The Other ◽  
Absolutely Continuous ◽  
Inversion Formulas ◽  
Tauberian Conditions ◽  
Tauberian Type ◽  
Necessary And Sufficient

AbstractWe study cosine and sine Fourier transforms defined by F(t):= (2/π) and (t):= (2/π), where f is L1-integrable over[0, ∞]. We also assume than F are locally absolutely continuous over [0, ∞). In particular, this is the case if both f(x) and xf(x) are (L1-integrable over [0, ∞). Motivated by the inversion formulas, we consider the partial integras Sν (f, x):= and ν(f, x):= , the modified partial integrals uν (f, x):= sν(f, x) - F(ν)(sin νx)/x and ũν(f, x):= ν(f, x) + (ν) (cos νx)/x, where ν > 0. We give necessary and sufficient conditions for(L1 [0, ∞)-convergence of uν (f) and ũν (f) as well as for the L1 [0, X]-convergence of sν (f) and ν(f) to f as ν← ∞, where 0 < X < ∞ is fixed. On the other hand, in certain cases we conclude that sν(f) and ν(f) cannot belong to (L1 [0,∞). Conequently, it makes no sense to speak of their (L1 [0, ∞)-convergence as ν ← ∞.As an intermediate tool, we use the Cesàro means of Fourier transforms. Then we prove Tauberian type results and apply Sidon type inequalities in order to obtain Tauberian conditions of Hardy-Karamata kind.We extend these results to the complex Fourier transform defined by G(t):= , where g is L1- integrable over (−∞, ∞).

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