A trace theorem for caloric functions (Q1070111)

In function theory, one extends an analytic function on a disk to the boundary while preserving continuity criteria. A first order modulus of continuity relates growth with smoothness of the boundary function when an extension exists. The author finds analogous results for classical solutions (caloric functions) of the heat equation on a strip \((- \infty,+\infty)\times (0,c).\) Necessary and sufficient conditions guarantee that a boundary function exists as a limit of a caloric function in a given weighted Banach space. A second order modulus of continuity links growth with smoothness at the boundary.