Mehler kernel

The Mehler kernel is a tool used to help mathematicians solve problems involving differential equations. It works by taking a function (like a graph of a curve, for example), and calculating how much that function will change when it is shifted or moved a little bit. This calculation is similar to the way a microscope takes a picture and then zooms in to see the details better. By zooming in on the details of a function, the Mehler kernel can help mathematicians understand it better and figure out how it will behave in different situations.