- journal articles metadata
European Mathematical Society Publishing House
2024-03-29 15:33:51
6
https://www.ems-ph.org/meta/jmeta-stream.php?jrn=RMI&vol=11&iss=1&update_since=2024-03-29
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)
11
1995
1
Estimates on the solution of an elliptic equation related to Brownian motion with drift
Joseph
Conlon
University of Michigan, ANN ARBOR, UNITED STATES
Juan
Redondo
University of Michigan, ANN ARBOR, UNITED STATES
General
1
65
10.4171/RMI/165
http://www.ems-ph.org/doi/10.4171/RMI/165
Formulas for approximate solutions of the $\partial \bar{\partial}$-equation in a strictly pseudoconvex domain
Mats
Andersson
Chalmers University of Technology, GOTHENBURG, SWEDEN
Hasse
Carlsson
Chalmers University of Technology, GOTHENBURG, SWEDEN
Let $D$ be a bounded strictly pseudoconvex domain in $\mathbb C^n$. We construct approximative solution formulas for the equation $i\partial \bar{\partial}u = \theta$, $\theta$ being an exact (1,1 )-form in $D$. We show that our formulas give simple proofs of known estimates and indicate further applications.
General
67
101
10.4171/RMI/166
http://www.ems-ph.org/doi/10.4171/RMI/166
Hiperbolic singular integral operators
Andrea
Nahmod
University of Massachusetts, AMHERST, UNITED STATES
We define a class of integral operators which are singular relative to the hyperbolic metric on simply connected domains of the plane. We study the necessary and sufficient conditions for such operators to be bounded on $L^2$ of the upper half plane relative to the hyperbolic metric.
General
103
123
10.4171/RMI/167
http://www.ems-ph.org/doi/10.4171/RMI/167
Fourier coefficients of Jacobi forms over Cayley numbers
Minking
Eie
National Chung Cheng University, CHIA-YI, TAIWAN
In this paper, we shall compute explicitly the Fourier coefficients of the Eisenstein series $$E_{k,m}(z,w) = \frac{1}{2} \sum \limits_{(c,d)=1} (cz + d)^{–k} \sum \limits_{t \in o} \mathrm {exp} \{ 2\pi im (\frac{az+b}{cz+d} N{t} + \sigma (t, \frac{w}{cz+d}) – \frac{cN(w)}{cz+d}) \}$$ which is a Jacobi form of weight $k$ and index $m$ defined on $\mathcal H \times \mathcal C_\mathbb C$, the product of the upper half-plane and Cayley numbers over the complex field $\mathbb C$. The coefficient of $e^{2 \pi i(nz+\sigma (t,w))}$ with $nm > N(t)$, has the form $$– \frac{2(k–4)}{B_{k–4}} \Pi_p S_p .$$ Here $S_p$ is an elementary factor which depends only on $\nu _p(m)$, $\nu _p (t)$, $\nu _p (n)$ and $\nu _p (nm–N(t))$. Also $S_p = 1$ for almost all $p$. Indeed, one has $S_p = 1$ if $\nu _p (m) = \nu _p (nm–N(t)) = 0$. An explicit formula for $S_p$ will be given in details. In particular, these Fourier coefficients are rational numbers.
General
125
142
10.4171/RMI/168
http://www.ems-ph.org/doi/10.4171/RMI/168
Trajectoires de groupes à 1-paramètre de quasi-isométries
Volker
Mayer
Université de Bordeaux I, TALENCE CEDEX, FRANCE
General
143
164
10.4171/RMI/169
http://www.ems-ph.org/doi/10.4171/RMI/169
Weyl sums and atomic energy oscillations
Antonio
Córdoba
Universidad Autónoma de Madrid, MADRID, SPAIN
Charles
Fefferman
Princeton University, PRINCETON, UNITED STATES
Luis
Seco
University of Toronto, TORONTO, ONTARIO, CANADA
We extend Van der Corput's method for exponential sums to study an oscillating term appearing in the quantum theory of large atoms. We obtain an interpretation in terms of classical dynamics and we produce sharp asymptotic upper and lower bounds for the oscillations.
General
165
226
10.4171/RMI/170
http://www.ems-ph.org/doi/10.4171/RMI/170