vero, e’ il preambolo del mio ex relatore, ma li ho tolti e in effetti non mi servono.
il mio secondo tentativo e’ stato quello di non numerare l’equazione incriminata e numerare quella dopo
(potevo permettermelo) ma a quel punto era l’equazione dopo a darmi lo stesso problema…
esempio minimo…. occhei copioeincollo parte del testo (scusa, non avevo capito):
\documentclass[11pt]{article}
\usepackage{amsfonts}
\usepackage{amsmath}
\usepackage[pdftex]{hyperref}
\usepackage{amsthm}
\usepackage{dsfont}
\usepackage{bbold}
\usepackage[english]{babel}
\usepackage{caption}
\usepackage{tensor}
\newcommand{\ZZZ}{\mathds{Z}}
\newcommand{\CCC}{\mathds{C}}
\newcommand{\NNN}{\mathds{N}}
\newcommand{\QQQ}{\mathds{Q}}
\newcommand{\RRR}{\mathds{R}}
\newcommand{\TTT}{\mathds{T}}
\newcommand{\uno}{\mathds{1}}
\newcommand{\la}{\lambda}
\newcommand{\ff}{\boldsymbol{f}}
\newcommand{\s}{\sigma}
\newcommand{\gotd}{{\mathfrak d}}
\newcommand{\gotC}{{\mathfrak C}}
\newcommand{\bvert}{\boldsymbol{\vert}}
\begin{document}
\section{Harmonic analysis on Lie Groups}
\label{sec.lie}
Denote by $w_{1},\ldots,w_{r}$ the fundamental weights of $G$
(see for instance [Pro]) and set
%
\begin{equation}\label{cono}
\Lambda_{+}(G):=\left\{j=\sum_{i=1}^{r}j_{i}w_{i}\,:\,
j_{i}\in\ZZZ_{+}\right\},
\end{equation}
%
i.e. the cone generated by the non-negative integer
linear combinations of the fundamental weights. If we denote also
%
\begin{equation}\label{rho}
\rho:=\sum_{i=1}^{r}w_{i}
\end{equation}
%
we can write the eigenvalues and the eigenfunctions of the
Laplace-Beltrami operator $\Delta$ on $G$ as
%
\begin{equation}\label{autov.lapla}
\la_{j}:=-\|j+\rho\|^{2}+\|\rho\|^{2},
\qquad
\ff_{j,\s}(x),
\quad
x\in G,
\quad
j\in\Lambda_{+}(G),
\quad
\s=1,\ldots,d_{j},
\end{equation}
%
where $\|\cdot\|$ is the euclidean norm on $\RRR^{\gotd}$,
$d_{j}\le \|j+\rho\|^{\gotd-r}$ is the \emph{degeneracy of the
eigenvalue} $\la_{j}$, and $\ff_{j}(x)$ is the (unitary) matrix
defined by
%
\begin{equation}\nonumber
(\ff_{j}(x))_{h,k}=\langle R_{V_{j}}(x)v_{h},v_{k}\rangle,
\qquad v_{h},v_{k} \in V_{j}
\end{equation}
%
if $(R_{V_{j}},V_{j})$ is an irreducible unitary representation of $G$.
Note that, for any $j\in\Lambda_{+}(G)$ one has $\|j+\rho\|\ge \|\rho\|$
and hence $\la_{j}\le0$.
\begin{lemma}[Lemma 2.6 of [BePro]]\label{stok}
$$
\|\rho\|, \|j\|^2…\in \gotC^{-1}\ZZZ
$$
\end{lemma}
Given $k=(l,j)\in\ZZZ^{d}\times \Lambda_{+}(G)$ we define also
\begin{equation}\label{bvertk}
\bvert k\bvert:=\max\left\{\max_{1\le i\le d}|l_{i}|,\max_{1\le i\le r}
|j_{i}|\right\}.
\end{equation}
\end{document}