Boundary values of zero solutions of hypoelliptic differential operators in ultradistribution spaces

Abstract

We study ultradistributional boundary values of zero solutions of a hypoelliptic constant coefficient partial differential operator $P(D)=P(D_x,D_t)$ on ${\mathbb{R}}^{d+1}$. Our work unifies and considerably extends various classical results of Komatsu and Matsuzawa about boundary values of holomorphic functions, harmonic functions and zero solutions of the heat equation in ultradistribution spaces. We also give new proofs of several results of Langenbruch [23] about distributional boundary values of zero solutions of $P(D)$.

31 pages

References in corpus (3)

• Almost analytic extensions of ultradifferentiable functions with applications to microlocal analysis
• On the extension of Whitney ultrajets, II
• An approximation theorem of Runge type for kernels of certain non-elliptic partial differential operators

Cited by in corpus (1)

• On generalized definitions of ultradifferentiable classes