<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">% \iffalse meta-comment
%
% Copyright (C) 2018 - 2021 by ChairX
%
% This file may be distributed and/or modified under the
% conditions of the LaTeX Project Public License, either
% version 1.3 of this license or (at your option) any later
% version.  The latest version of this license is in:
%
%    http://www.latex-project.org/lppl.txt
%
% and version 1.3 or later is part of all distributions of
% LaTeX version 2005/12/01 or later.
%
% This file contains the implementation of all analysis related macros .
%
% Macros have to be described by (delete the first %)
% %\begin{macro}{\macro}
% % Description of the implementation.
% %    \begin{macrocode}
%\newcommand{\macro}[]         {}
% %    \end{macrocode}
% %\end{macro}
%
% The implementation and description will appear in the implementation
% part of the documentation. Use \subsubsection{} etc. for structuring.
%
% The documentation of the macros defined here has to be written in
% chairxmathAnalysisDoc.dtx
%\fi
%
% First we check of macros should be included:
%    \begin{macrocode}
\if@loadmath
%    \end{macrocode}
%
% \subsubsection{General Analysis} \label{sec:GeneralMacrosAnalysis}
%
%\begin{macro}{\vol}
%    \begin{macrocode}
\newcommand{\vol}{\ch@irxoperatorfont{vol}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\complete}
%    \begin{macrocode}
\newcommand{\complete}[1]{\widehat{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Ball}
%    \begin{macrocode}
\newcommand{\Ball}{\ch@irxoperatorfont{B}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\abs}
%    \begin{macrocode}
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\norm}
%    \begin{macrocode}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\supnorm}
%    \begin{macrocode}
\newcommand{\@supnormstar}[1]{\norm*{#1}_\infty}
\newcommand{\@supnormnostar}[2][]{\norm[#1]{#2}_\infty}
\newcommand{\supnorm}{\@ifstar\@supnormstar\@supnormnostar}
%    \end{macrocode}
%\end{macro}
%
% \begin{macro}{\expands}
%    \begin{macrocode}
\newcommand{\expands}[1][2.5]{\mathrel{\scalebox{#1}[1.1]{$\sim$}}}
%    \end{macrocode}
% \end{macro}
%
%
% \subsubsection{Pseudodifferential Operators}
%
% \begin{macro}{\std}
%    \begin{macrocode}
\newcommand{\std}{{\scriptscriptstyle{\ch@irxscriptfont{std}}}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\Weyl}
%    \begin{macrocode}
\newcommand{\Weyl}{{\scriptscriptstyle{\ch@irxscriptfont{Weyl}}}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\Op}
%    \begin{macrocode}
\newcommand{\Op}{\operatorname{Op}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\Opstd}
%    \begin{macrocode}
\newcommand{\Opstd}{\operatorname{Op}_\std}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\OpWeyl}
%    \begin{macrocode}
\newcommand{\OpWeyl}{\operatorname{Op}_\Weyl}
%    \end{macrocode}
% \end{macro}
%
%
%\subsubsection{Function Spaces}
%
% \begin{macro}{\spacename}
%     \begin{macrocode}
\newcommand{\spacename}[1]{\ch@irxspacefont{#1}}
%    \end{macrocode}
% \end{macro}
%
%\begin{macro}{\Bounded}
%    \begin{macrocode}
\newcommand{\Bounded}{\ch@irxspacefont{B}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Continuous}
%    \begin{macrocode}
\newcommand{\Continuous}{\ch@irxspacefont{C}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Contbound}
%    \begin{macrocode}
\newcommand{\Contbound}{\Continuous_{\mathrm{b}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Fun}
%    \begin{macrocode}
\newcommand{\Fun}[1][k]{\ch@irxspacefont{C}^{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Cinfty}
%    \begin{macrocode}
\newcommand{\Cinfty}{\Fun[\infty]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Comega}
%    \begin{macrocode}
\newcommand{\Comega}{\Fun[\omega]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Holomorphic}
%    \begin{macrocode}
\newcommand{\Holomorphic}{\ch@irxspacefont{O}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\AntiHolomorphic}
%    \begin{macrocode}
\newcommand{\AntiHolomorphic}{\cc{\Holomorphic}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Schwartz}
%    \begin{macrocode}
\newcommand{\Schwartz}{\ch@irxspacefont{S}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Riemann}
%    \begin{macrocode}
\newcommand{\Riemann}{\ch@irxspacefont{R}}
%    \end{macrocode}
%\end{macro}
%
%
%\subsubsection{Locally Convex Spaces}
%
%\begin{macro}{\singsupp}
%    \begin{macrocode}
\newcommand{\singsupp}{\operatorname{sing\,supp}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\seminorm}
%    \begin{macrocode}
\newcommand{\seminorm}[1]{\mathrm{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\ord}
%    \begin{macrocode}
\newcommand{\ord}{\operatorname{ord}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\conv}
%    \begin{macrocode}
\newcommand{\conv}{\operatorname{conv}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\extreme}
%    \begin{macrocode}
\newcommand{\extreme}{\operatorname{extreme}}
%    \end{macrocode}
%\end{macro}
%
%
%\subsubsection{Hilbert Spaces}
%
%\begin{macro}{\hilbert}
%    \begin{macrocode}
\newcommand{\hilbert}[1]{\ch@irxhilbertfont{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\prehilb}
%    \begin{macrocode}
\newcommand{\prehilb}[1]{\ch@irxprehilbfont{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Adjointable}
%    \begin{macrocode}
\newcommand{\Adjointable}[1][{}]{\mathfrak{B}_{\scriptscriptstyle{#1}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Finite}
%    \begin{macrocode}
\newcommand{\Finite}[1][{}]{\mathfrak{F}_{\scriptscriptstyle{#1}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Compact}
%    \begin{macrocode}
\newcommand{\Compact}[1][{}]{\mathfrak{K}_{\scriptscriptstyle{#1}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\opdomain}
%    \begin{macrocode}
\newcommand{\opdomain}{\ch@irxhilbertfont{D}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\spec}
%    \begin{macrocode}
\newcommand{\spec}{\operatorname{\ch@irxoperatorfont{spec}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\closure}
%    \begin{macrocode}
\newcommand{\closure}[1]{\overline{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\res}
%    \begin{macrocode}
\newcommand{\res}{\operatorname{\ch@irxoperatorfont{res}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Res}
%    \begin{macrocode}
\newcommand{\Res}{\operatorname{\ch@irxoperatorfont{Res}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\specrad}
%    \begin{macrocode}
\newcommand{\specrad}{\operatorname{\varrho}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\slim}
%    \begin{macrocode}
\newcommand{\slim}{\operatorname*{\ch@irxoperatorfont{s-lim}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\wlim}
%    \begin{macrocode}
\newcommand{\wlim}{\operatorname*{\ch@irxoperatorfont{w-lim}}}
%    \end{macrocode}
%\end{macro}
%
%
%\subsubsection{Dirac's bra and ket}
%
%\begin{macro}{\bra}
%\begin{macro}{\ket}
%\begin{macro}{\braket}
%\begin{macro}{\ketbra}
%    \begin{macrocode}
\DeclarePairedDelimiter{\ketbr@}{\vert}{\vert}
\DeclarePairedDelimiter{\ket}{\vert}{\rangle}
\DeclarePairedDelimiter{\bra}{\langle}{\vert}
\newcommand{\braket}[3][]{\SP[#1]{#2 \,#1\vert\, #3}}
\newcommand{\ketbra}[3][]{\ketbr@[#1]{#2 #1\rangle #1\langle #3}}
%    \end{macrocode}
%\end{macro}
%\end{macro}
%\end{macro}
%\end{macro}
%
%
%\subsubsection{Operator Algebras}
%
%\begin{macro}{\Spec}
%    \begin{macrocode}
\newcommand{\Spec}{\operatorname{\ch@irxoperatorfont{Spec}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Rad}
%    \begin{macrocode}
\newcommand{\Rad}{\operatorname{\ch@irxoperatorfont{Rad}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\ind}
%    \begin{macrocode}
\newcommand{\ind}{\operatorname{\ch@irxoperatorfont{ind}}}
%    \end{macrocode}
%\end{macro}
%
%
%\subsubsection{Measure Theory and Integration}
%
%\begin{macro}{\Measurable}
%    \begin{macrocode}
\newcommand{\Measurable}{\ch@irxspacefont{M}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Meas}
%    \begin{macrocode}
\newcommand{\Meas}{\ch@irxoperatorfont{Meas}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\BoundMeas}
%    \begin{macrocode}
\newcommand{\BoundMeas}{\ch@irxspacefont{BM}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Lp}
%    \begin{macrocode}
\newcommand{\Lp}[1][{p}]{\mathrm{L}^{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Lone}
%    \begin{macrocode}
\newcommand{\Lone}{\Lp[1]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Ltwo}
%    \begin{macrocode}
\newcommand{\Ltwo}{\Lp[2]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Linfty}
%    \begin{macrocode}
\newcommand{\Linfty}{\Lp[\infty]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Intp}
%    \begin{macrocode}
\newcommand{\Intp}[1][{p}]{\ch@irxspacefont{L}^{#1}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Intone}
%    \begin{macrocode}
\newcommand{\Intone}{\Intp[1]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Inttwo}
%    \begin{macrocode}
\newcommand{\Inttwo}{\Intp[2]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\Intinfty}
%    \begin{macrocode}
\newcommand{\Intinfty}{\Intp[\infty]}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\essrange}
%    \begin{macrocode}
\newcommand{\essrange}{\operatorname{\ch@irxoperatorfont{ess\,range}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\esssup}
%    \begin{macrocode}
\newcommand*{\esssup}{\operatorname*{\ch@irxoperatorfont{ess}\,\ch@irxoperatorfont{\sup}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\esssupnormstar}
%    \begin{macrocode}
\newcommand{\@esssupnormstar}[1]{\norm*{#1}_{\esssup}}
\newcommand{\@esssupnormnostar}[2][]{\norm[#1]{#2}_{\esssup}}
\newcommand{\esssupnorm}{\@ifstar\@esssupnormstar\@esssupnormnostar}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\ac}
%    \begin{macrocode}
\newcommand{\ac}{\ch@irxscriptfont{ac}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\sing}
%    \begin{macrocode}
\newcommand{\sing}{\ch@irxscriptfont{sing}}
%    \end{macrocode}
%\end{macro}
%
% \subsubsection{Limits} \label{sec:Limits}
%
%\begin{macro}{\indlim}
%    \begin{macrocode}
\newcommand{\indlim}{\operatorname*{{ind\,lim}}}
%    \end{macrocode}
%\end{macro}
%
%\begin{macro}{\projlim}
%    \begin{macrocode}
\renewcommand{\projlim}{\operatorname*{{proj\,lim}}}
%    \end{macrocode}
%\end{macro}
%
%    \begin{macrocode}
\fi
%    \end{macrocode}</pre></body></html>