Related papers: Re-parameterizing and reducing families of normal …

Let $P(x,z)= z^d +\sum_{i=1}^{d}a_i(x)z^{d-i}$ be a polynomial, where $a_i$ are real analytic functions in an open subset $U$ of $\R^n$. If for any $x \in U$ the polynomial $z\mapsto P(x,z)$ has only real roots, then we can write those…

We construct of a family of fundamental solutions for elliptic partial differential operators with real constant coefficients. The elements of such a family are expressed by means of jointly real analytic functions of the coefficients of…

We propose an extension of the one dimensional (doubling) renormalization operator to the case of maps on the cylinder. The kind of maps considered are commonly referred as quasi-periodic forced one dimensional maps. We prove that the fixed…

We examine the precise connection between the exact renormalisation group with local couplings and the renormalisation of correlation functions of composite operators in scale-invariant theories. A geometric description of theory space…

We give conditions for local diagonalization of an analytic operator family to a diagonal operator polynomial. The families are acting between real or complex Banach spaces. The basic assumption is given by stabilization of the Jordan…

We present a general form of Renormalization operator $\mathcal{R}$ acting on potentials $V:\{0,1\}^\mathbb{N} \to \mathbb{R}$. We exhibit the analytical expression of the fixed point potential $V$ for such operator $\mathcal{R}$. This…

In this article, we prove the existence of rigid analytic families of $G$-stable lattices with locally constant reductions inside families of representations of a topologically compact group $G$, extending a result of Hellman obtained in…

We introduce a unified framework based on bi-level optimization schemes to deal with parameter learning in the context of image processing. The goal is to identify the optimal regularizer within a family depending on a parameter in a…

We construct a renormalization operator which acts on analytic circle maps whose critical exponent $\alpha$ is not necessarily an odd integer $2n+1$, $n\in\mathbb N$. When $\alpha=2n+1$, our definition generalizes cylinder renormalization…

Generalized analytic functions over generalized analytic manifolds are build from sums of convergent real power series with non-negative real exponents (and some well-ordering condition on the support). In a paper by Mart\'in-Villaverde,…

We study the period doubling renormalization operator for dynamics which present two coupled laminar regimes with two weakly expanding fixed points. We focus our analysis on the potential point of view, meaning we want to solve…

We gain tight rigorous bounds on the renormalisation fixed point for period doubling in families of unimodal maps with degree $4$ critical point. We use a contraction mapping argument to bound essential eigenfunctions and eigenvalues for…

We establish an algorithm for a criterion of the diagonalisability of a matrix over a local field by a unitary matrix. For this sake, we define the notion of normality of a $p$-adic operator, and give several criteria for the normality. We…

We study a particular class of families of multi-dimensional lattice Schr\"o\-dinger operators with deterministic (including quasi-periodic) potentials generated by the "hull" given by an orthogonal series over the Haar wavelet basis on the…

In the paper we prove that there exists a simultaneous reduction of one-parameter family of $\mathfrak{m}_{n}$-primary ideals in the ring of germs of holomorphic functions. As a corollary we generalize the result of A. P\l{}oski…

We give conditions for local diagonalization of analytic operator families acting between real or complex Banach spaces. The transformations are constructed from an operator Toeplitz matrix obtained from Jordan chains of increasing length.…

We study the dynamics of the renormalization operator acting on the space of pairs (v,t), where v is a diffeomorphism and t belongs to [0,1], interpreted as unimodal maps x-->v(q_t(x)), where q_t(x)=-2t|x|^a+2t-1. We prove the so called…

We consider holomorphic maps defined in an annulus around $\mathbb R/\mathbb Z$ in $\mathbb C/\mathbb Z$. E. Risler proved that in a generic analytic family of such maps $f_\zeta$ that contains a Brjuno rotation $f_0(z)=z+\alpha$, all maps…

We gain tight rigorous bounds on the renormalisation fixed point function for period doubling in families of unimodal maps with degree 2 critical point. By writing the relevant eigenproblems in a modified nonlinear form, we use these…

Arnold, Falk, & Winther, in "Finite element exterior calculus, homological techniques, and applications" (2006), show how to geometrically decompose the full and trimmed polynomial spaces on simplicial elements into direct sums of…