Probability Error Bounds for Approximation of Functions in Reproducing Kernel Hilbert Spaces
نویسندگان
چکیده
We find probability error bounds for approximations of functions f in a separable reproducing kernel Hilbert space id="M2"> H with id="M3"> K on base id="M4"> X , firstly terms finite linear combinations type id="M5"> x i and then the projection id="M6"> π n id="M7"> span = 1 random sequences points id="M8"> open="(" close=")"> id="M9"> . Given measure id="M10"> P letting id="M11"> be defined by id="M12"> d , id="M13"> ∈ our approach is based nonexpansive operator id="M14"> L 2 ; ∋ λ ↦ ≔ ∫ where integral exists Bochner sense. Using this operator, we define new space, denoted id="M15"> that range id="M16"> Our main result establishes bounds, id="M17"> distance between an arbitrary function id="M18"> id="M19"> id="M20"> id="M21"> sampled independently from id="M22"> falls below given threshold. For id="M23"> ∞ constituting so-called uniqueness set, orthogonal projections id="M24"> to id="M25"> converge strong topology identity operator. prove that, under assumption id="M26"> dense id="M27"> any sequence id="M28"> yields set 1. This improves previous weaker norms, such as uniform or id="M29"> p which yield only convergence not almost certain convergence. Two examples show applicability distribution compact interval Hardy id="M30"> H mathvariant="double-struck">D are presented well.
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ژورنال
عنوان ژورنال: Journal of function spaces
سال: 2021
ISSN: ['2314-8896', '2314-8888']
DOI: https://doi.org/10.1155/2021/6617774