## Jón Áskell Þorbjarnarson (29/02/16)

Math Colloquium – BS project

### Speaker: Jón Áskell Þorbjarnarson.

Title: Distributions and fundamental solutions of partial differential equations

Location: V02-157 , VRII

Time: Friday, January 29, at 15:00-16:00.

### Abstract:

We discuss distributions, which are generalisations of integrable functions on Rn. We define them as linear functionals on the space of smooth functions with compact support. Distributions are infinitely differentiable in a weaker sense than in classical analysis and provide a larger space of solutions to differential equations. We discuss fundamental solutions of differential equations which enable us to find solutions to inhomogeneous equations using convolution. We calculate fundamental solutions for a few operators from mathematical physics and finally prove the existence theorem of Ehrenpreis & Malgrange which states that every partial differential operator with constant coefficients has a fundamental solution.