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- Title
Bandlimited Approximations to the Truncated Gaussian and Applications.
- Authors
Carneiro, Emanuel; Littmann, Friedrich
- Abstract
In this paper, we extend the theory of optimal approximations of functions f:ℝ→ℝ in the L(ℝ)-metric by entire functions of prescribed exponential type (bandlimited functions). We solve this problem for the truncated and the odd Gaussians using explicit integral representations and properties of truncated theta functions obtained via the maximum principle for the heat operator. As applications, we recover most of the previously known examples in the literature and further extend the class of truncated and odd functions for which this extremal problem can be solved, by integration on the free parameter and the use of tempered distribution arguments. This is the counterpart of the work (Carneiro et al. in Trans. Am. Math. Soc., ), where the case of even functions is treated.
- Subjects
APPROXIMATION theory; GAUSSIAN function; DETERMINISTIC algorithms; MATHEMATICAL literature; EXTREMAL problems (Mathematics); MATHEMATICAL programming
- Publication
Constructive Approximation, 2013, Vol 38, Issue 1, p19
- ISSN
0176-4276
- Publication type
Article
- DOI
10.1007/s00365-012-9177-8