International Journal of Mathematics and Mathematical Sciences 
Volume 8 (1985), Issue 1, Pages 29-35
doi:10.1155/S0161171285000023

A trace theorem for Caloric functions

H. N. Mhaskar

 Department of Mathematics and Computer Science, California State University, Los Angeles 90032, California, USA
Received 4 August 1983

Abstract

Given a solution of the heat equation in an open strip, we state necessary and sufficient conditions for the existence of a boundary function in a given weighted Banach space. We then investigate the relationship between the smoothness of this boundary function and the growth of the solution of the heat equation.