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Asymptotic Separation of Variables

Authors
Journal
Journal of Mathematical Analysis and Applications
0022-247X
Publisher
Elsevier
Publication Date
Volume
178
Issue
1
Identifiers
DOI: 10.1006/jmaa.1993.1296

Abstract

Abstract We study generalized functions ƒ( x) that admit the asymptotic separation of variables ƒ(λx) ∼ ρ 1(λ)h 1(x) + ρ 2(λ)h 2(x) + ρ 3(λ)h 3(x) + ···, as λ → ∞, where {ρ n (λ)} is an asymptotic sequence. Among other results, we show that when the asymptotic separation of variables holds, the terms have to be homogeneous and associated homogeneous generalized functions. The asymptotic expansion of ρ(λ x), as λ → ∞, where ρ is a regularly varying function, is also considered.

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