KTH/SU Mathematics Colloquium
05-02-23
Jan-Erik Björk, SU
Fundamental solution to PDE's and the Weyl algebra
The aim of this talk is to show that interplay
between analysis and algebra often is very fruitful.
To construct a tempered fundamental solution to a
differential operator P(D) with constant coefficients
means , via the Fourier transform, that
the polynomial P(z) is inverted in the space
S'(R^n) of tempered distributions.
To find such an inverse one uses algebraic results
about the Weyl Algebra A_n which is the non-commutative algebra of
differential operators with polynomial coefficients.
Some results due to Sato and Bernstein will be exposed
together with some specific examples such as the construction of
fundamental solutions to PDE's of real principal type
with an optimal small analytic wave front set.