On the completeness of Gaussians in a Hilbert functional space
Victor Katsnelson
TL;DR
This paper proves that Gaussian functions form a complete set in a Hilbert functional space, ensuring they can represent any element within that space.
Contribution
It provides a theoretical proof of the completeness of Gaussians in a specific Hilbert space, advancing understanding of their functional properties.
Findings
Gaussians are complete in the Hilbert space
The proof establishes foundational properties for Gaussian-based representations
Supports future research in Gaussian approximation methods
Abstract
The completeness of Gaussians in a Hilbert functional space is established
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