TFPT scientific source excerpt
Original repository path: documents/archive--tfpt-45--source_extracts--01_boundary_kernel_source/sections/001-section-primitive-core-and-carrier-interface-handoff.tex
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000109 | \]
000110 | on the Cauchy-data Hilbert space $\mathcal H_{\partial}$.
000111 | 
000112 | Then:
000113 | \begin{enumerate}[label=(\roman*), leftmargin=1.8em, topsep=3pt, itemsep=2pt]
000114 |     \item the geometric objects are
000115 |     \[
000116 |     M=\widetilde M/\taudbl,
000117 |     \qquad
000118 |     \Seam=\mathrm{Fix}(\taudbl),
000119 |     \qquad
000120 |     \Xbulk=\widetilde M\setminus\Seam;
000121 |     \]
000122 |     \item the doubled operator and its even and odd parts are
000123 |     \[
000124 |     D=D_+\cup_{\Sigma}D_+^{\mathrm{op}},
000125 |     \qquad
000126 |     D_{\mathrm{ref}}:=\frac12\bigl(D+\taudbl^{\ast}D\taudbl^{\ast}\bigr),
000127 |     \qquad
000128 |     D_{\mathrm{rel}}:=\frac12\bigl(D-\taudbl^{\ast}D\taudbl^{\ast}\bigr);
000129 |     \]
000130 |     \item on boundary Cauchy data the induced reflection $R_{\taudbl}$ satisfies
000131 |     \[
000132 |     \operatorname{Ran}(P_C)=\ker(R_{\taudbl}-1),
000133 |     \qquad
000134 |     \ker(P_C)=\ker(R_{\taudbl}+1),
000135 |     \qquad