diff options
author | Karl Berry <karl@freefriends.org> | 2021-08-08 21:00:57 +0000 |
---|---|---|
committer | Karl Berry <karl@freefriends.org> | 2021-08-08 21:00:57 +0000 |
commit | eec3a67f3a57872862cf4adee13eeddc981d5442 (patch) | |
tree | cb82517f4d28e8f9d61ab18d1993595d6fc23ebc /Master/texmf-dist/source/latex/nchairx/chairxmathAnalysisDoc.dtx | |
parent | 3de8aad561c3a6fb16971dc6c7f68c189e8c4dc1 (diff) |
nchairx (8aug21)
git-svn-id: svn://tug.org/texlive/trunk@60196 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/source/latex/nchairx/chairxmathAnalysisDoc.dtx')
-rw-r--r-- | Master/texmf-dist/source/latex/nchairx/chairxmathAnalysisDoc.dtx | 297 |
1 files changed, 297 insertions, 0 deletions
diff --git a/Master/texmf-dist/source/latex/nchairx/chairxmathAnalysisDoc.dtx b/Master/texmf-dist/source/latex/nchairx/chairxmathAnalysisDoc.dtx new file mode 100644 index 00000000000..43954d61d66 --- /dev/null +++ b/Master/texmf-dist/source/latex/nchairx/chairxmathAnalysisDoc.dtx @@ -0,0 +1,297 @@ +% \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 documentation of all analysis related macros . +% +% Macros have to be described by (delete the first %) +% \DescribeMacro{\macro} +% Description and usage of the macro. +% +% The description will appear in the usage +% part of the documentation. Use \subsubsection{} etc. for structuring. +% +% The implementation of the macros defined here has to be written in +% chairxmathAnalysis.dtx +%\fi +% +%\subsubsection{General Anyalsis Macros} \label{sec:Doc_GeneralMacrosAnalysis} +% +% \DescribeMacro{\vol} +% Volume |\vol|: $\vol$\\ +% Uses |operatorfont| +% +% \DescribeMacro{\complete} +% Completion of some space |\complete{V}|: $\complete{V}$ +% +% \DescribeMacro{\Ball} +% Open ball |\Ball_{r}(p)|: $\Ball_{r}(p)$ +% +% \DescribeMacro{\abs} +% Generic absolute value |\abs{x}|: $\abs{x}$ +% +% \DescribeMacro{\norm} +% Generic norm |\norm{v}|: $\norm{v}$ +% +% \DescribeMacro{\supnorm} +% Supremum norm |\supnorm{f}|: $\supnorm{f}$ +% +% \DescribeMacro{\expands} +% Formal expansions |f(t) \stackrel{t \to 0}{\expands} t^k|: +% $f(t) \stackrel{t \to 0}{\expands} t^k$, \\ +% or with optional stretching factor (default is 2.5) |a \expands[4] b|: $a \expands[4] b$. +% +% +% \subsubsection{Pseudodifferential Operators} +% \label{sec:Doc_PseudodifferentialOperators} +% +% \DescribeMacro{\std} +% Standard ordering as small subscript |\sigma_\std|: $\sigma_\std$ \\ +% Uses |scriptfont| +% +% \DescribeMacro{\Weyl} +% Weyl ordering as small subscript |\sigma_\Weyl|: $\sigma_\Weyl$ \\ +% Uses |scriptfont| +% +% \DescribeMacro{\Op} +% Operator for a symbol |\Op(f)|: $\Op(f)$ \\ +% Uses |operatorfont| +% +% \DescribeMacro{\Opstd} +% Standard ordered operator for a symbol |\Opstd(f)|: $\Opstd(f)$ \\ +% Uses |operatorfont| +% +% \DescribeMacro{\OpWeyl} +% Weyl ordered operator for a symbol |\OpWeyl(f)|: $\OpWeyl(f)$ \\ +% Uses |operatorfont| +% +% +%\subsubsection{Function Spaces} +% +% \DescribeMacro{\spacename} +% Font for specific functional spaces |\spacename{F}(X)|: $\spacename{F}(X)$ \\ +% Uses |spacefont|. +% +% \DescribeMacro{\Bounded} +% Bounded functions |\Bounded(X)|: $\Bounded(X)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\Continuous} +% Continuous functions |\Continuous(X)|: $\Continuous(X)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\Contbound} +% Continuous bounded functions |\Contbound(X)|: $\Contbound(X)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\Fun} +% $C^k$-functions (for $\Continuous$ use |\Continuous|) |\Fun(M)|: $\Fun(M)$ and |\Fun[\ell](M)|: $\Fun[\ell](M)$ \\ +% Uses |spacefont|. +% +% \DescribeMacro{\Cinfty} +% Smooth functions |\Cinfty|: $\Cinfty(M)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\Comega} +% Real-analytic functions |\Comega|: $\Comega(M)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\Holomorphic} +% Holomorphic functions |\Holomorphic|: $\Holomorphic(U)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\AntiHolomorphic} +% Anti-holomorphic functions |\AntiHolomorphic|: $\AntiHolomorphic(U)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\Schwartz} +% Schwartz space |\Schwartz|: $\Schwartz(\mathbb{R}^n)$\\ +% Uses |spacefont|. +% +% \DescribeMacro{\Riemann} +% Riemann integrable functions |\Riemann([a, b])|: $\Riemann([a, b])$ \\ +% Uses |spacefont|. +% +% \subsubsection{Locally Convex Analysis and Distributions} +% +% \DescribeMacro{\singsupp} +% Singular support of a distribution |\singsupp u|: $\singsupp u$ +% +% \DescribeMacro{\seminorm} +% Font for generic seminorm |\seminorm{p}|: $\seminorm{p}$ +% +% \DescribeMacro{\ord} +% Order of a distribution |\ord(u)|: $\ord(u)$ +% +% \DescribeMacro{\conv} +% Convex hull |\conv(A)|: $\conv(A)$ +% +% \DescribeMacro{\extreme} +% Extreme points |\extreme(A)|: $\extreme(A)$ +% +% \subsubsection{Hilbert Spaces and Operators} +% +% \DescribeMacro{\hilbert} +% Font for Hilbert spaces |\hilbert{H}|: $\hilbert{H}$ \\ +% Uses |hilbertfont| +% +% \DescribeMacro{\prehilb} +% Font for pre-Hilbert spaces |\prehilb{H}|: $\prehilb{H}$ \\ +% Uses |prehilbfont|. +% +% \DescribeMacro{\Adjointable} +% Adjointable operators |\Adjointable(\hilbert{H})|: +% $\Adjointable(\hilbert{H})$ or with optional argument +% |\Adjointable[\algebra{A}](\hilbert{H})|: $\Adjointable[\algebra{A}](\hilbert{H})$ if +% we have a Hilbert module over an algebra $\algebra{A}$ instead. +% +% \DescribeMacro{\Finite} +% Finite rank operators |\Finite(\hilbert{H})|: $\Finite(\hilbert{H})$ +% or with optional argument +% |\Finite[\algebra{A}](\module{H})|: $\Finite[\algebra{A}](\module{H})$ +% +% \DescribeMacro{\Compact} +% Compact operators |\Compact(\hilbert{H})|: $\Compact(\hilbert{H})$ +% or with optional argument +% |\Compact[\algebra{A}](\module{H})|: $\Compact[\algebra{A}](\module{H})$ +% +% \DescribeMacro{\opdomain} +% Domain of definition of an operator |\opdomain(A)|: $\opdomain(A)$ \\ +% Uses |\hilbertfont|. +% +% \DescribeMacro{\spec} +% Spectrum of an operator |\spec(A)|: $\spec(A)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\closure} +% Closure of an operator |\closure{A}|: $\closure{A}$ +% +% \DescribeMacro{\res} +% Resolvent set of an operator |\res(A)|: $\res(A)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\Res} +% Resolvent of an operator |\Res_z(A)|: $\Res_z(A)$\\ +% Uses |operatorfont|. +% +% \DescribeMacro{\specrad} +% Spectral radius of an operator |\specrad(A)|: $\specrad(A)$ +% +% \DescribeMacro{\slim} +% Strong limit |\slim_{n \longrightarrow \infty} A_n|: $\slim_{n \longrightarrow \infty} A_n$ +% +% \DescribeMacro{\wlim} +% Weak limit |\wlim_{n \longrightarrow \infty} A_n|: $\wlim_{n \longrightarrow \infty} A_n$ +% +% \subsubsection{Dirac's Bra and Ket Notation} +% +% \DescribeMacro{\bra} +% Dirac bra |\bra{\psi}|: $\bra{\psi}$ +% +% \DescribeMacro{\ket} +% Dirac ket |\ket{\phi}|: $\ket{\phi}$ +% +% \DescribeMacro{\braket} +% Dirac braket |\braket{\phi}{\psi}|: $\braket{\phi}{\psi}$ +% +% \DescribeMacro{\ketbra} +% Dirac ketbra |\ketbra{\phi}{\psi}|: $\ketbra{\phi}{\psi}$ +% +% \subsubsection{Operator Algebras} +% +% \DescribeMacro{\Spec} +% Spectrum of an algebra |\Spec(\algebra{A})|: $\Spec(\algebra{A})$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\Rad} +% Radical of an algebra |\Rad(\algebra{A})|: $\Rad(\algebra{A})$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\ind} +% Fredholm index (|\index| is already used!) |\ind(A)|: $\ind(A)$ \\ +% Uses |operatorfont|. +% +% \subsubsection{Measure Theory and Integration} +% +% Here we need various function space of integrable functions +% (calligraphic ones) and the corresponding quotients by zero +% functions (roman ones): +% +% \DescribeMacro{\Measurable} +% Measurable functions |\Measurable(X)|: $\Measurable(X)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\Meas} +% Complex measures |\Meas(X)|: $\Meas(X)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\BoundMeas} +% Bounded measurable functions |\BoundMeas(X)|: $\BoundMeas(X)$ \\ +% Uses |spacefont|. +% +% \DescribeMacro{\Lp} +% Equivalence classes of $p$-integrable functions ($p$ is an optional +% argument) |\Lp(X)|: $\Lp(X)$ and |\Lp[q](X)|: $\Lp[q](X)$ +% +% \DescribeMacro{\Lone} +% Equivalence classes of integrable functions |\Lone(X)|: $\Lone(X)$ +% +% \DescribeMacro{\Ltwo} +% Equivalence classes of square integrable functions |\Ltwo(X)|: $\Ltwo(X)$ +% +% \DescribeMacro{\Linfty} +% Equivalence classes of essentially bounded functions |\Linfty(X)|: $\Linfty(X)$ +% +% \DescribeMacro{\Intp} +% Space of $p$-integrable functions |\Intp(X)|: +% $\Intp(X)$ and with optional argument +% |\Intp[q](X)|: $\Intp[q](X)$ +% +% \DescribeMacro{\Intone} +% Space of integrable functions |\Intone(X)|: $\Intone(X)$ +% +% \DescribeMacro{\Inttwo} +% Space of square integrable functions |\Inttwo(X)|: $\Inttwo(X)$ +% +% \DescribeMacro{\Intinfty} +% Space of essentially bounded functions |\Intinfty(X)|: $\Intinfty(X)$ +% +% \DescribeMacro{\essrange} +% Essential range |\essrange(f)|: $\essrange(f)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\esssup} +% Essential supremum |\esssup(f)|: $\esssup(f)$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\esssupnorm} +% Essential supremum norm |\esssupnorm{f}|: $\esssupnorm{f}$ \\ +% Uses |operatorfont|. +% +% \DescribeMacro{\ac} +% Absolutely continuous part of a measure |\mu_\ac|: $\mu_\ac$ \\ +% Uses |scriptfont|. +% +% \DescribeMacro{\sing} +% Singular part of a measure |\mu_\sing|: $\mu_\sing$ \\ +% Uses |scriptfont|. +% +% \subsubsection{Limits} \label{sec:Doc_Limits} +% +%\DescribeMacro{\indlim} +% Inductive (or direct) limit |\indlim_{i \in I} A_i|: $\indlim_{i \in I} A_i$\\ +% Uses |operatorfont|. +% +%\DescribeMacro{\projlim} +% Projective (or inverse) limit |\projlim_{i \in I} A_i|: $\projlim_{i \in I} A_i$\\ +% Uses |operatorfont|.
\ No newline at end of file |