Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets

Download original file

This is the original TeX manuscript source. Use the paper’s PDF for typeset equations.

Read the typeset paper

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\fontsize{10}{12}\selectfont #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,before skip=6pt,after skip=5pt,fontupper=\fontsize{10}{12}\selectfont}
10 \providecommand{\takeaway}[1]{\begin{insight}\textbf{Read this as:}\ #1\end{insight}}
11 \providecommand{\vfig}[2][.92]{\par\begingroup\centering\resizebox{#1\linewidth}{!}{\input{visual_graphics/#2.tex}}\par\endgroup\vspace{2pt}}
12 
13 \newif\ifstarted\startedfalse
14 \providecommand{\vpage}[4]{\ifstarted\clearpage\else\startedtrue\fi
15 \pdfbookmark[1]{V#1. #2}{plate#1}\hypertarget{vpage#1}{}\phantomsection\label{visual:#1}
16 {\sffamily\fontsize{9}{11}\selectfont\bfseries\color{accent}V#1\quad /\quad #3\par}\vspace{5pt}
17 {\sffamily\bfseries\fontsize{19}{22}\selectfont #2\par}\vspace{5pt}
18 {\sffamily\fontsize{8.7}{11}\selectfont\color{muted} #4\par}\vspace{6pt}}
19 \providecommand{\pagerefV}[1]{\hyperlink{vpage#1}{V#1}}
20 
21 \providecommand{\CC}{\mathbb C}
22 \providecommand{\kk}{\mathbb k}
23 \renewcommand{\AA}{\mathcal A}
24 \providecommand{\BB}{\mathcal B}
25 \providecommand{\Hull}{\operatorname{Hull}}
26 \providecommand{\srank}{\operatorname{srank}}
27 \providecommand{\Span}{\operatorname{span}}
28 \providecommand{\End}{\operatorname{End}}
29 \providecommand{\diag}{\operatorname{diag}}
30 \providecommand{\Ker}{\operatorname{ker}}
31 \providecommand{\norm}[1]{\left\lVert#1\right\rVert}
32 \providecommand{\mat}[1]{\begin{pmatrix}#1\end{pmatrix}}
33 
34 

Back to source controls

Back to Paper II: Refinement Towers, Weighted Transfer, and Integral Separation of Operator Packets