chapter  15
10 Pages

The Green Function of the Hermite Operator

Thus, the Green function of the Hermite operator is the function G on Rn×Rn given by

G(x, y) = ∑ α∈Nn0

2|α|+ 1eα(x)eα(y) (15.2)

for all x and y in Rn. In fact,

G(x, y) =

Ht(x, y) dt

= 1

πn

Remark 15.1 The formula for the Green function in integral form is not as tractable as one expects. It is the series (15.2) that turns out to be more useful for the Hermite operator.