Rectifiability of solutions of the one-dimensional -Laplacian.
Recursive inset entropies of multiplicative type on open domains.
Reduction of semialgebraic constructible functions
Let R be a real closed field with a real valuation v. A ℤ-valued semialgebraic function on Rⁿ is called algebraic if it can be written as the sign of a symmetric bilinear form over R[X₁,. .., Xₙ]. We show that the reduction of such a function with respect to v is again algebraic on the residue field. This implies a corresponding result for limits of algebraic functions in definable families.
Refined measurable rigidity and flexibility for conformal iterated function systems.
Refinement of the Shannon-McMillan-Breiman theorem for some maps of an interval
Refinement type equations: sources and results
It has been proved recently that the two-direction refinement equation of the form can be used in wavelet theory for constructing two-direction wavelets, biorthogonal wavelets, wavelet packages, wavelet frames and others. The two-direction refinement equation generalizes the classical refinement equation , which has been used in many areas of mathematics with important applications. The following continuous extension of the classical refinement equation has also various interesting applications....
Reformulation et extension de certains théorèmes ergodiques
Regular generators for multidimensional dynamical systems
Regular mappings between dimensions
The notions of Lipschitz and bilipschitz mappings provide classes of mappings connected to the geometry of metric spaces in certain ways. A notion between these two is given by regular mappings (reviewed in Section 1), in which some non-bilipschitz behavior is allowed, but with limitations on this, and in a quantitative way. In this paper we look at a class of mappings called (s, t)-regular mappings. These mappings are the same as ordinary regular mappings when s = t, but otherwise they behave somewhat...
Regular measures and entropy on pseudo-compact spaces
Regular measures and normal lattices.
Regular variation for measures on metric spaces.
Régularité des bases d'ondelettes et mesures ergodiques.
Nous reprenons la construction des bases orthonormées d'ondelettes à partir des filtres miroirs en quadrature tel qu'elle apparaît dans [4]. Nous montrons que leur régularité est liée à une mesure invariante pour la transformation ω → 2ω mod-2π. Cette méthode permet d'obtenir le facteur exact qui relie asymptotiquement la régularité des ondelettes constriutes dans [4] à la taille de leur support.
Regularities of distribution
Regularity and Approximation Theorems for Measures and Integrals
Regularity of pre-random measures
Regularity of semigroup-valued set functions
Regularity of sets with constant intrinsic normal in a class of Carnot groups
In this Note, we define a class of stratified Lie groups of arbitrary step (that are called “groups of type ” throughout the paper), and we prove that, in these groups, sets with constant intrinsic normal are vertical halfspaces. As a consequence, the reduced boundary of a set of finite intrinsic perimeter in a group of type is rectifiable in the intrinsic sense (De Giorgi’s rectifiability theorem). This result extends the previous one proved by Franchi, Serapioni & Serra Cassano in step...
Regularity properties of functional equations.
Regularity properties of functional equations. (Short Communication).