Schwartz Distribution Theory

Schwartz Distribution Theory is a mathematical framework that extends traditional concepts of functions to include "distributions," which are generalized objects that can represent things like impulses or point sources. Instead of focusing solely on values at specific points, it allows us to analyze and manipulate objects like the Dirac delta function, which is useful in physics and engineering. This theory enables more complex mathematical operations and gives meaning to differential equations that wouldn’t otherwise have solutions, thus broadening the scope of analysis in various scientific fields.