Manuscript XV-B@2 · XV-B.tex · definition · 4d3f12e8

Definition: Reconstruction interface

Reconstruction and the exact relative-lifting criterion › The linear interface · lines 337–366

XV-B@2#def:interface, XV-B@2#eq:prelift

Let $P_{int}$ be a vector space and let

Rec : P_{int} ⟶ K_{int}

be a surjective linear map. Set

H = ker Rec, K_{int} = im Rec .

Let $O \subset W$ be open, and put

V = D^{'} (W; E_{res}), V_{O} = D^{'} (O; E_{res}) .

Let $r : V \to V_{O}$ be restriction, and let

m^{\circ} : K_{int} ⟶ V_{O}

be a prescribed linear canonical map. Define

c = m^{\circ} Rec, Y = ker r .

A preliminary lift is a linear map $F_{0} : P_{int} \to V$ satisfying

r F_{0} = c .

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