For we have for the differential dilation operator,

where again . This follows from row 2 of the matrix . In the Dirichlet BC case this becomes,

The integral is proportional to the matrix element of the billiard dilation deformation.

No general form for has been found. The
corresponding unit vector
does not lie in
the row space of
, indicating that other boundary
derivatives are needed as input.
However, for the particular case of Dirichlet BCs and there exists the
simple formula

(H.26) |