Translation-based completeness on compact intervals
Year: 2024
Type: article
Abstract: Given a compact interval I ⊆ R , and a function f that is a product of a nonzero polynomial with a Gaussian, it will be shown that the translates { f ( ⋅ − λ ) : λ ∈ Λ } are complete in C ( I ) if and only if the series of reciprocals of Λ diverges. This extends a theorem in [R. A. Zalik, Trans. Amer. Math. Soc. 243, 299–308]. An additional characterization is obtained when Λ is an arithmetic progression, and the generator f constitutes a linear combination of translates of a function with sufficiently fast decay.
Source: Journal of Approximation Theory
Author: Lukas Liehr
Institution: University of Vienna
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,830
OpenAlex ID: W4402946006