The infinitestimal operator for the semigroup of the Frobenius-Perron operator from image sequence data: Vector fields and computational measurable dynamics from movies

Compact weighted Frobenius-Perron operators and their spectra

In this note we characterize the compact weighted Frobenius-Perron operator $p$ on $L^1(Sigma)$ and determine their spectra. We also show that every weakly compact weighted Frobenius-Perron operator on $L^1(Sigma)$ is compact.

Weighted Frobenius-Perron and Koopman operators

Operator Valued Series and Vector Valued Multiplier Spaces

‎Let $X,Y$ be normed spaces with $L(X,Y)$ the space of continuous‎ ‎linear operators from $X$ into $Y$‎. ‎If ${T_{j}}$ is a sequence in $L(X,Y)$,‎ ‎the (bounded) multiplier space for the series $sum T_{j}$ is defined to be‎ [ ‎M^{infty}(sum T_{j})={{x_{j}}in l^{infty}(X):sum_{j=1}^{infty}%‎ ‎T_{j}x_{j}text{ }converges}‎ ‎]‎ ‎and the summing operator $S:M^{infty}(sum T_{j})rightarrow Y$ associat...

Performance Bounds for Dispersion Analysis: A Comparison Between Monte Carlo and Perron-Frobenius Operator Approach

We compare computational cost and accuracy between two different approaches of dispersion analysis. One is the conventional Monte Carlo method and the other being the Perron-Frobenius operator approach, that directly propagates the joint probability density function using Liouville equation. It is shown that with same computational budget, Perron-Frobenius operator approach rewards better accur...

A set oriented definition of finite-time Lyapunov exponents and coherent sets

The problem of phase space transport, which is of interest from both the theoretical and practical point of view, has been investigated extensively using geometric and probabilistic methods. Two important tools to study this problem that have emerged in recent years are finite-time Lyapunov exponents (FTLE) and the Perron–Frobenius operator. The FTLE measures the averaged local stretching aroun...