Distribution theory on P.C.F. fractalsJournal d'Analyse Mathematique - Tập 112 - Trang 137-191 - 2011
Luke G. Rogers, Robert S. Strichartz
We construct a theory of distributions in the setting of analysis on post-critically finite self-similar fractals, and on fractafolds and products based on such fractals. The results include basic properties of test functions and distributions, a structure theorem showing that distributions are locally-finite sums of powers of the Laplacian applied to continuous functions, and an analysis of the d...... hiện toàn bộ
Rigidity of groups of circle diffeomorphisms and teichmüller spacesJournal d'Analyse Mathematique - - 2020
Katsuhiko Matsuzaki
We consider deformations of a group of circle diffeomorphisms with Hölder continuous derivative in the framework of quasiconformal Teichmüller theory and showcertain rigidity under conjugation by symmetric homeomorphisms of the circle. As an application, we give a condition for such a diffeomorphism group to be conjugate to a Möbius group by a diffeomorphism of the same regularity. The strategy is...... hiện toàn bộ
Unique continuation through transversal characteristic hypersurfacesJournal d'Analyse Mathematique - Tập 138 - Trang 135-156 - 2019
Nicolas Lerner
We prove a unique continuation result for an ill-posed characteristic problem. A model problem of this type occurs in the A. D. Ionescu and S. Klainerman article (Theorem 1.1 in [11]) and we extend their model-result using only geometric assumptions. The main tools are Carleman estimates and Hörmander’s pseudo-convexity conditions.
Bernstein functions and rates in mean ergodic theorems for operator semigroupsJournal d'Analyse Mathematique - - 2012
Alexander Gomilko, Markus Haase, Yuri Tomilov
We present a functional calculus approach to the study of rates of decay in mean ergodic theorems for bounded strongly continuous operator semigroups. A central role is played by operators of the form g(A, where −A is the generator of the semigroup and g is a Bernstein function. In addition, we obtain some new results on Bernstein functions which are of independent interest.
Uniform estimates on multi-linear operators with modulation symmetryJournal d'Analyse Mathematique - Tập 88 - Trang 255-309 - 2002
Camil Muscalu, Terence Tao, Christoph Thiele
In a previous paper [20] in this series, we gaveL
p estimates for multi-linear operators given by multipliers which are singular on a non-degenerate subspace of some dimensionk. In this paper, we give uniform estimates when the subspace approaches a degenerate region in the casek = 1, and when all the exponentsp are between 2 and ∞. In particular, we recover the non-endpoin...... hiện toàn bộ
Quasiconformal extension of biholomorphic mappings in several complex variablesJournal d'Analyse Mathematique - Tập 96 - Trang 269-282 - 2005
Hidetaka Hamada, Gabriela Kohr
Letf(z, t) be a subordination chain fort ∈ [0, α], α>0, on the Euclidean unit ballB inC
n. Assume thatf(z) =f(z, 0) is quasiconformal. In this paper, we give a sufficient condition forf to be extendible to a quasiconformal homeomorphism on a neighbourhood of
$$\bar B$$
. We also s...... hiện toàn bộ