Related papers: A Floquet-Liapunov theorem in Frechet spaces
In this paper, a new rigorous numerical method to compute fundamental matrix solutions of non-autonomous linear differential equations with periodic coefficients is introduced. Decomposing the fundamental matrix solutions $\Phi(t)$ by their…
In this paper, a general hybrid fixed point theorem for the contractive mappings in generalized Banach spaces is proved via measure of weak non-compactness and it is further applied to fractional integral equations for proving the existence…
In this work we investigate the functional differentiability of the time-dependent many-body wave function and of derived quantities with respect to time-dependent potentials. For properly chosen Banach spaces of potentials and wave…
The aim of the present paper is twofold:(1) We carry on with developing an abstract method for deriving decay estimates on the semigroup associated to non-symmetric operators in Banach spaces as introduced in [10]. We extend the method so…
For every filter $\mathcal F$ on $\mathbb N$, we introduce and study corresponding uniform $\mathcal F$-boundedness principles for locally convex topological vector spaces. These principles generalise the classical uniform boundedness…
We consider the Cauchy problem for the Gross-Pitaevskii infinite linear hierarchy of equations on $\mathbb{R}^n.$ By introducing a (F)-norm in certain Sobolev type spaces of sequences of marginal density matrices, we establish local…
We show an abstract time-periodic bifurcation theorem in Banach spaces. The key point as well as the novelty of the method is to split the original evolution equation into two different coupled equations, one for the time-average of the…
We establish the Kolmogorov-Feller weak law of large numbers for Frechet mean on non-compact symmetric spaces under certain regularity conditions. Our results accommodate non-identically distributed random variables and are accompanied by…
We prove a Frobenius theorem for Banach distributions on manifolds that are modelled over locally convex spaces. Moreover, we recall how Frobenius theorems can be applied to infinite-dimensional Lie groups and obtain, that given a Lie…
Fr\'echet mean and variance provide a way of obtaining mean and variance for general metric space valued random variables and can be used for statistical analysis of data objects that lie in abstract spaces devoid of algebraic structure and…
This is the first of a series of papers concerned with principal Lyapunov exponents and principal Floquet subspaces of positive random dynamical systems in ordered Banach spaces. It focuses on the development of general theory. First, the…
This paper introduces a notion of differential forms on closed, potentially fractal, subsets of Euclidean space by defining pointwise cotangent spaces using the restriction of $C^1$ functions to this set. Aspects of cohomology are…
The classical Floquet theory allows to map a time-periodic system of linear differential equations into an autonomous one. By looking at it in a geometrical way, we extend the theory to a class of non-autonomous non-periodic equations. This…
We analyse and compare several algorithms to compute numerically periodic solutions of high-dimensional dynamical systems and investigate their Floquet stability without building the monodromy matrix. The solution and its perturbation are…
We discuss an alternative approach to Fr\'echet derivatives on Banach spaces inspired by a characterisation of derivatives due to Carath\'eodory. The approach allows us to reduce many questions of differentiability to a question of…
We prove strong convergence theorems of some iterative algorithms in a real uniformly smooth Banach space. The results presented extend, generalize and improve the corresponding results recently announced by many authors.
We consider the problem of estimating the Fr\'echet and conditional Fr\'echet mean from data taking values in separable metric spaces. Unlike Euclidean spaces, where well-established methods are available, there is no practical estimator…
In this paper we establish some new results concerning the Cauchy-Peano problem in Banach spaces. Firstly, we prove that if a Banach space $E$ admits a fundamental biorthogonal system, then there exists a continuous vector field $f\colon…
We present a constructive proof of Floquet's theorem for the special case of unitary time evolution in quantum mechanics. The proof is straightforward and suitable for study in courses on quantum mechanics.
We study an infinite system of ordinary differential equations that models the evolution of coagulating and fragmenting clusters, which we assume to be composed of identical units. Under very mild assumptions on the coefficients we prove…