Abstract. We consider continuity theorems for multiplicative integral transforms $\hat{f}$ of functions $f\colon(0, \infty ) \to{\msbm R},$ i.e., we relate the limit behaviours $f_n \to f$ with $\hat{f_n} \to\hat {f}.$ These continuity theorems based on sequential compactness arguments lead to Abelian-- and ratio--Tauberian theorems for these integral transforms.
AMS Subject Classification
(1991): 44A05, 40E05
Keyword(s):
Integral transform,
continuity theorems,
Abelian theorems,
Tauberian theorems,
dominated variation,
regular variation
Received January 29, 1999. (Registered under 2707/2009.)
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