Poisson kernel

Imagine you have a circle on a piece of paper. Now, you want to draw a line from the center of the circle to one of the points on the outside of the circle. There are many different ways you could do this, but the Poisson kernel is a special way of doing it that follows some particular rules.

First, the Poisson kernel makes sure that the line you draw from the center to the point reaches the outer edge of the circle at a right angle (like a T shape). Second, the Poisson kernel says that the length of the line you draw should be proportional to the distance between the center of the circle and the point you want to draw the line to.

So, if you think of the circle as representing some mathematical function (like a temperature map, for example), the Poisson kernel can be used to create a new function that tells you how much heat or energy is flowing from the center of the circle out to each point on the edge.

Overall, the Poisson kernel is just a fancy tool that mathematicians use to help them understand certain mathematical problems, like figuring out how much heat is flowing through a certain area or how quickly data is spreading across a network. But even if you're just drawing circles on a piece of paper, it's a neat trick to know!