Linearizations via Dirac delta function

Yue Yu

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arXiv · 2306.10074

Linearizations via Dirac delta function

Yue Yu

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Abstract

This note is to show that the position-space embedding in \cite{ESP2021embedding} in the position and occupation bases can be obtained by considering the dynamics of Dirac delta function $$δ(\mathbf{x}- \mathbf{z}(t)) = δ(x_1-z_1(t))\cdots δ(x_d-z_d(t)),$$ where $\mathbf{z}(t)\in \mathbb{R}^d$ is the solution of a nonlinear dynamical system and $\mathbf{x}\in \mathbb{R}^d$ is a variable in the position space.

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Yue Yu. 2023-06-26. Linearizations via Dirac delta function. https://arxiv.org/abs/2306.10074

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