- journal articles metadata
European Mathematical Society Publishing House
2024-03-28 23:22:12
8
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=12&iss=1&update_since=2024-03-28
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
12
1996
1
Wavelets obtained by continuous deformations of the Haar wavelet
Aline
Bonami
Université d'Orléans, ORLÉANS CEDEX 2, FRANCE
Sylvain
Durand
Université d'Orléans, ORLÉANS CEDEX 2, FRANCE
Guido
Weiss
Washington University in St. Louis, ST. LOUIS, UNITED STATES
One might obtain the impression, from the wavelet literature, that the class of orthogonal wavelets is divided into subclasses, like compactly supported ones on one side, band-limited ones on the other side. The main purpose of this work is to show that, in fact, the class of low-pass filters associated with "reasonable" (in the localization sense, not necessarily in the smooth sense) wavelets can be considered to be an infinite dimensional manifold that is arcwise connected. In particular, we show that any such wavelet can be connected in this way to the Haar wavelet.
General
1
18
10.4171/RMI/191
http://www.ems-ph.org/doi/10.4171/RMI/191
The spin of the ground state of an atom
Charles
Fefferman
Princeton University, PRINCETON, UNITED STATES
Luis
Seco
University of Toronto, TORONTO, ONTARIO, CANADA
General
19
36
10.4171/RMI/192
http://www.ems-ph.org/doi/10.4171/RMI/192
Correspondances géodésiques entre les surfaces euclidiennes à singularités coniques
Mohammed Mostefa
Mesmoudi
Université de Strasbourg, STRASBOURG CEDEX, FRANCE
A.J. Montesinos has shown that a geodesic correspondence between to complete Riemannian manifolds with transitive topological geodesic flow is a homothety. In this paper we prove a similar result for a conformal geodesic correspondence between two singular flat surfaces with conical singularities and negative concentrated curvature.
General
37
45
10.4171/RMI/193
http://www.ems-ph.org/doi/10.4171/RMI/193
The range of Toeplitz Operators on the ball
Boris
Korenblum
State University of New York, ALBANY, UNITED STATES
John
McCarthy
Washington University in St. Louis, ST. LOUIS, UNITED STATES
General
47
61
10.4171/RMI/194
http://www.ems-ph.org/doi/10.4171/RMI/194
Generalized Fock spaces, interpolation, multipliers, circle geometry
Jaak
Peetre
Lund University, LUND, SWEDEN
Sundaram
Thangavelu
Indian Institute of Science, BANGALORE, INDIA
Nils-Olof
Wallin
Lund University, LUND, SWEDEN
By a (generalized) Fock space we understand a Hilbert space of entire analytic functions in the complex plane $\mathbb C$ which are square integrable with respect to a weight of the type $e^{–Q(z)}$, where $Q(z)$ is a quadratic form such that tr$Q>0$. Each such space is in a natural way associated with an (oriented) circle $C$ in $\mathbb C$. We consider the problem of interpolation betweeumn two Fock spaces. If $C_0$ and $C_1$ are the corresponding circles, one is led to consider the pencil of circles generated by $C_0$ and $C_1$. If $H$ is the one parameter Lie group of Moebius transformations leaving invariant the circles in the pencil, we consider its complexification $H^c$ which permutes these circles and with the aid of which we can construct the "Calderón curve" giving the complex interpolation. Similarly, real interpolation leads to a multiplier problem for the transforrnation that diagonalizes all the operators in $H^c$. It turns out that the result is rather sensitive to the nature of the pencil, and we obtain nearly complete results for elliptic and parabolic pencils only.
General
63
110
10.4171/RMI/195
http://www.ems-ph.org/doi/10.4171/RMI/195
On fractional differentiation and integration on spaces of homogeneous type
A. Eduardo
Gatto
DePaul University, CHICAGO, UNITED STATES
Carlos
Segovia
Universidad de Buenos Aires, BUENOS AIRES, ARGENTINA
Stephen
Vági
DePaul University, CHICAGO, UNITED STATES
In this paper we define derivatives of fractional order on spaces of homogeneous type by generalizing a classical formula for the fractional powers of the Laplacean [S1], [S2], [SZ] and introducing suitable quasidistances related to an approximation of the identity. We define integration of fractional order as in [GV] but using quasidistances related to the approximation of the identity mentioned before. We show that these operators act on Lipschitz spaces as in the classical cases. We prove that the composition $T_\alpha$ of a fractional integral $I_\alpha$ and a fractional derivative $D_\alpha$ of the same order and its transpose (a fractional derivative composed with a fractional integral of the same order) are Calderón-Zygmund operators. We also prove that for small order $\alpha$a, $T_\alpha$ is an invertible operator in $L^2$. In order to prove that $T_\alpha$ is invertible we obtain Nahmod type representations for $I_\alpha$ and $D_\alpha$ and then we follow the method of her thesis [N1], [N2].
General
111
145
10.4171/RMI/196
http://www.ems-ph.org/doi/10.4171/RMI/196
The heat kernel on Lie groups
Pierre
Charollois
Université Paris 6 Pierre et Marie Curie, PARIS CEDEX 05, FRANCE
General
147
186
10.4171/RMI/197
http://www.ems-ph.org/doi/10.4171/RMI/197
Good metric spaces without good parameterizations
Stephen
Semmes
Rice University, HOUSTON, UNITED STATES
A classical problem in geometric topology is to recognize when a topological space is a topological manifold. This paper addresses the question of when a rnetric space admits a quasisymmetric parameterization by providing counterexamples to the obvious optimistic conjectures, or, in other words, by providing examples of spaces with many Euclidean-like properties which are nonetheless substantially different from Euclidean geometry. These examples are geometrically self-similar versions of classical topologically self-similar examples from geometric topology, and they can be realized as codimension 1 subsets of Euclidean spaces. Unlike earlier examples going back to Rickman, these sets enjoy good bounds on their geodesic distance functions and good mass bounds (AhIfors regularity). They are also smooth except for reasonably tame degenerations near small sets, they are uniform1y rectifiable, and they have good properties in terms of analysis (like Sobolev and Poincaré inequalities). The construction also produces uniform domains which have many nice properties but which are not quasiconformally equivalent to balls.
General
187
275
10.4171/RMI/198
http://www.ems-ph.org/doi/10.4171/RMI/198