Odd-order obstruction for scalar elliptic operators in at least three dimensions
= Odd-order obstruction for scalar elliptic operators in at least three dimensions
{title2=$n\geq3\Rightarrow N\text{ even}$}
The <principal symbol> of an odd-order scalar <differential operator> is an odd map from the frequency <sphere> to the complex plane. The <Borsuk-Ulam theorem> forces a zero on a two-dimensional <sphere>, contradicting ellipticity. Restriction to three variables proves the same obstruction in every greater dimension.