atlas-definitions.tex

Paper VI: Transfer Semigroups: Stochastic, Bayesian, Fractional, and PDE Realizations

atlas-definitions.tex

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1 \providecommand{\OO}{\mathcal O}
2 \providecommand{\FF}{\mathbb F}\providecommand{\QQ}{\mathbb Q}\providecommand{\ZZ}{\mathbb Z}\providecommand{\RR}{\mathbb R}
3 \providecommand{\Spec}{\operatorname{Spec}}\providecommand{\Supp}{\operatorname{Supp}}\providecommand{\Fitt}{\operatorname{Fitt}}
4 \providecommand{\Ann}{\operatorname{Ann}}\providecommand{\coker}{\operatorname{coker}}\providecommand{\im}{\operatorname{im}}
5 \providecommand{\rank}{\operatorname{rank}}\providecommand{\Tr}{\operatorname{Tr}}\providecommand{\id}{\operatorname{id}}
6 \providecommand{\whot}{\mathbin{\widehat\otimes}}\providecommand{\m}{\mathfrak m}\providecommand{\p}{\mathfrak p}
7 \providecommand{\head}[1]{\par\vspace{2pt}{\sffamily\bfseries\normalsize #1}\par\vspace{1pt}}
8 \providecommand{\platecaption}[1]{\par\noindent{\footnotesize\color{black!70}#1\par}}
9 \newtcolorbox{insight}{colback=accent!3,colframe=accent,boxrule=0pt,leftrule=1.1pt,arc=0pt,left=10pt,right=10pt,top=5pt,bottom=5pt,fontupper=\fontsize{10.5}{12.6}\selectfont,before skip=6pt,after skip=5pt}
10 \providecommand{\takeaway}[1]{\begin{insight}\textbf{Read this as:}\ #1\end{insight}}
11 \providecommand{\vfig}[2][.92]{\par\begingroup\renewcommand{\arraystretch}{1.5}\centering\resizebox{#1\linewidth}{!}{\input{visual_graphics/#2.tex}}\par\endgroup\vspace{2pt}}
12 \newif\ifstarted\startedfalse
13 \providecommand{\vpage}[4]{\ifstarted\clearpage\else\startedtrue\fi
14 \pdfbookmark[1]{V#1. #2}{vplate#1}\hypertarget{vvpage#1}{}\label{vvisual:#1}
15 {\sffamily\fontsize{9}{11}\selectfont\bfseries\color{accent}V#1\quad /\quad #3\par}\vspace{5pt}
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17 {\sffamily\fontsize{8.7}{11}\selectfont\color{muted} #4\par}\vspace{6pt}}
18 \providecommand{\pagerefV}[1]{\hyperlink{vvpage#1}{V#1}}
19 
20 \providecommand{\CC}{\mathbb C}
21 \providecommand{\kk}{\mathbb k}
22 \providecommand{\AA}{\mathcal A}
23 \providecommand{\BB}{\mathcal B}
24 \providecommand{\Hull}{\operatorname{Hull}}
25 \providecommand{\srank}{\operatorname{srank}}
26 \providecommand{\Span}{\operatorname{span}}
27 \providecommand{\End}{\operatorname{End}}
28 \providecommand{\diag}{\operatorname{diag}}
29 \providecommand{\Ker}{\operatorname{ker}}
30 \providecommand{\norm}[1]{\left\lVert#1\right\rVert}
31 \providecommand{\mat}[1]{\begin{pmatrix}#1\end{pmatrix}}
32 \providecommand{\Ob}{\operatorname{Ob}}
33 \providecommand{\supp}{\operatorname{supp}}
34 \providecommand{\src}{\operatorname{src}}\providecommand{\tgt}{\operatorname{tgt}}
35 \providecommand{\Res}{\operatorname{Res}}
36 \providecommand{\sech}{\operatorname{sech}}
37 \providecommand{\Dfun}{\mathsf D}
38 \providecommand{\Efun}{\mathsf E}
39 \providecommand{\Tfun}{\mathsf T}
40 \providecommand{\Sfun}{\mathsf S}
41 \providecommand{\Cfun}{\mathsf C}
42 \providecommand{\Thetafun}{\symup{\Theta}}
43 \providecommand{\ones}{\mathbf{1}}
44 \providecommand{\EE}{\mathbb{E}}
45 \providecommand{\Var}{\operatorname{Var}}
46 \providecommand{\diagmat}[1]{\operatorname{diag}(#1)}
47 

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