Based on [4], we prove a variation of the theorem in title, for equations with periodic coefficients, in Fréchet spaces. The main result gives equivalent conditions ensuring the reduction of such an equation to one with constant coefficient. In the particular case of C ∞ , we obtain the exact analogue of the classical theorem. Our approach essentially uses the fact that a Fréchet space is the l...

A new methodology leading to the construction of a universal connection for Fréchet principal bundles is proposed in this paper. The classical theory, applied successfully so far for finite dimensional and Banach modelled bundles, collapses within the framework of Fréchet manifolds. However, based on the replacement of the space of continuous linear mappings by an appropriate topological vector...

We discuss two versions of the Fréchet distance problem in weighted planar subdivisions. In the first one, the distance between two points is the weighted length of the line segment joining the points. In the second one, the distance between two points is the length of the shortest path between the points. In both cases, we give algorithms for finding a (1 + ǫ)-factor approximation of the Fréch...

Based on the methods from interpolation theory we give a characterization of pairs (E,F ) of Fréchet-Hilbert spaces so that for each Fréchet-Hilbert space G each short exact sequence 0 −→ F −→ G −→ E −→ 0 splits. This characterization essentially depends on a key condition (S) of an interpolation nature. An equivalent description of (S) in terms of appropriate families of interpolation function...

We revisit the problem of computing the Fréchet distance between polygonal curves, focusing on the discrete Fréchet distance, where only distance between vertices is considered. We develop efficient approximation algorithms for two natural classes of curves: κ-bounded curves and backbone curves, the latter of which are widely used to model molecular structures. We also propose a pseudo–output-s...

In order to use persistence diagrams as a true statistical tool, it would be very useful to have a good notion of mean and variance for a set of diagrams. In [21], Mileyko and his collaborators made the first study of the properties of the Fréchet mean in (Dp,Wp), the space of persistence diagrams equipped with the p-th Wasserstein metric. In particular, they showed that the Fréchet mean of a f...

The Fréchet distance is a popular and widespread distance measure for point sequences and for curves. About two years ago, Agarwal et al [SIAM J. Comput. 2014] presented a new (mildly) subquadratic algorithm for the discrete version of the problem. This spawned a flurry of activity that has led to several new algorithms and lower bounds. In this paper, we study the approximability of the discre...

Abstract.— We describe the use of the Fréchet mean and variance in the Billera-Holmes-Vogtmann (BHV) treespace to summarize and explore the diversity of a set of phylogenetic trees. We show that the Fréchet mean is comparable to other summary methods, despite its stickiness property, and that the Fréchet variance is faster and more precise than commonly used variance measures. These mean and va...