On Wavelet Fundamental Solutions to the Heat Equation—Heatlets

We present an application of wavelet theory in partial differential equations. We study the wavelet fundamental solutions to the heat equation. The heat evolution of an initial wavelet state is called a heatlet. Like wavelets for the L2 space, heatlets are “atomic” heat evolutions in the sense that any general heat evolution can be “assembled” from a heatlet according to some simple rules. We study the basic properties and algorithms of heatlets and related functions.