% $Header: /cvsroot/latex-beamer/latex-beamer/solutions/conference-talks/conference-ornate-20min.en.tex,v 1.7 2007/01/28 20:48:23 tantau Exp $

\documentclass{beamer}

% This file is a solution template for:

% - Talk at a conference/colloquium.
% - Talk length is about 20min.
% - Style is ornate.



% Copyright 2004 by Till Tantau <tantau@users.sourceforge.net>.
%
% In principle, this file can be redistributed and/or modified under
% the terms of the GNU Public License, version 2.
%
% However, this file is supposed to be a template to be modified
% for your own needs. For this reason, if you use this file as a
% template and not specifically distribute it as part of a another
% package/program, I grant the extra permission to freely copy and
% modify this file as you see fit and even to delete this copyright
% notice.

\mode<presentation>
{
  \usetheme{Warsaw}
  % or ...
\color{red}
  %\setbeamercovered{transparent}
  % or whatever (possibly just delete it)
}


\usepackage[english]{babel}
% or whatever

\usepackage[latin1]{inputenc}
% or whatever

\usepackage{times}
\usepackage[T1]{fontenc}
% Or whatever. Note that the encoding and the font should match. If T1
% does not look nice, try deleting the line with the fontenc.

\title[My 495 Project] % (optional, use only with long paper titles)
{Localization and Finite Frames}

\author[My Name] % (optional, use only with lots of authors)
{My Name}
% - Give the names in the same order as the appear in the paper.
% - Use the \inst{?} command only if the authors have different
%   affiliation.

\institute[ University of North Carolina at Wilmington] % (optional, but mostly needed)
{

  Department of Mathematics and Statistics\\
  University of North Carolina at Wilmington}

% - Use the \inst command only if there are several affiliations.
% - Keep it simple, no one is interested in your street address.

\date[2010] % (optional, should be abbreviation of conference name)
{From Banach spaces to Frame Theory and Applications, Norbert Wiener Center 2010 \\  \textbf{Collaborators}:\\Blum,G\"unt\"urk, Fickus,Maeser,Powell,Saab, Y{\i}lmaz }

% - Either use conference name or its abbreviation.
% - Not really informative to the audience, more for people (including
%   yourself) who are reading the slides online


% This is only inserted into the PDF information catalog. Can be left
% out.



% If you have a file called "university-logo-filename.xxx", where xxx
% is a graphic format that can be processed by latex or pdflatex,
% resp., then you can add a logo as follows:

% \pgfdeclareimage[height=0.5cm]{university-logo}{university-logo-filename}
% \logo{\pgfuseimage{university-logo}}

\newtheorem{thm}{Theorem}[section]
\newtheorem{prop}[thm]{Proposition}
\newtheorem{hyp}[thm]{Hypothesis}
\newtheorem{cor}[thm]{Corollary}
\newtheorem{lem}[thm]{Lemma}
\newtheorem{res}[thm]{Result}
\newtheorem{defn}[thm]{Definition}
\newtheorem{rem}[thm]{Remark}
\newtheorem{conj}[thm]{Conjecture}
\newtheorem{exam}[thm]{Example}
 \newcommand{\bd}{$ \begin{displaystyle}}
\newcommand{\ed}{\end{displaystyle} $ }

% Delete this, if you do not want the table of contents to pop up at
% the beginning of each subsection:
\AtBeginSubsection[]
{
  \begin{frame}<beamer>{Outline}
    \tableofcontents[currentsection,currentsubsection]
  \end{frame}
}


% If you wish to uncover everything in a step-wise fashion, uncomment
% the following command:

%\beamerdefaultoverlayspecification{<+->}


\begin{document}

\frame{\titlepage}
%\begin{frame}
%\frametitle{Overview}
%\begin{itemize}
%\item \textbf{Time-Frequency Measures Continuous Case}\\ Sobolev \\Gauss-Hermite\\ Balian-Low
%
%\item \textbf{Finite Frequency Measure}\\Sigma Delta \\Sobolev Dual  \\ Example
%
%\item \textbf{Finite Time-Frequency Measures} \\ Parseval Frames \\Time Frequency Duals \\ Example
%
%\end{itemize}
%\end{frame}




\begin{frame}  \frametitle{Finite Time-Frequency Localization }

For \bd D_c, \Delta,\ed and  \bd \mathcal F\ed \bd N \times N\ed matrices: \pause

\vspace{.3in}

\textbf{Finite Time Frequency measure for ${\bf f}\in \mathbb C^N$:}
\begin{align*} \|D_c{\bf f}\|^2+\|D_c \mathcal F{\bf f}\|^2&=\langle D_c {\bf f}, D_c{\bf f}\rangle + \langle D_c \mathcal F{\bf f}, D_c\mathcal F{\bf f}\rangle  \\&=\begin{color}{blue}\langle(\Delta+ \mathcal F^* \Delta \mathcal F){\bf f}, {\bf f}\rangle\end{color}\end{align*}


\pause

Can be used to produce Hermite functions for \bd \mathbb C^N \ed.

Here is a reference \cite{BF}


\end{frame}

\begin{frame}\frametitle{References}

{\tiny \bibliographystyle{alpha}
\bibliography{ff-tf} }
\end{frame}
\end{document}




