In this paper, we derive the eigenfunctions of the Fourier transform (FT), the fractional FT (FRFT), and the linear canonical transform (LCT) with (1) complex parameters and (2) complex offsets. The ...

The subject of Prof. Titchmarsh's book is the expansion of an arbitrary function in terms of the eigenfunctions of linear differential equations; to be precise, in terms of functions which satisfy ...

We present the Quantum Section Method as a quantization technique to compute the eigenvalues and the eigenfunctions of quantum systems. As an instructive example we apply this procedure to quantize ...

This article develops data-driven methods to identify eigenfunctions of the Koopman operator associated with a dynamical system and subspaces that are invariant under the operator. We build on ...

Thus, the leading eigenvalues are to be associated with the longest implied timescales, meaning that their corresponding eigenfunctions have a slow relaxation toward the equilibrium. For this reason, ...

Mapping out the high-dimensional state space would be valuable for better understanding the multistate quantum systems. Here, we demonstrate that high-dimensional spin state space can be mapped onto a ...

neural networks to learn Koopman eigenfunctions. Contribute to BethanyL/DeepKoopman development by creating an account on GitHub.