Search results for "Ultradistribution"
showing 3 items of 3 documents
ω-hypoelliptic differential operators of constant strength
2004
Abstract We study ω-hypoelliptic differential operators of constant strength. We show that any operator with constant strength and coefficients in E ω (Ω) which is homogeneous ω-hypoelliptic is also σ-hypoelliptic for any weight function σ=O(ω). We also present a sufficient condition in order to ensure that a differential operator admits a parametrix and, as a consequence, we obtain some conditions on the weights (ω,σ) to conclude that, for any operator P(x,D) with constant strength, the σ-hypoellipticity of the frozen operator P(x0,D) implies the ω-hypoellipticity of P(x,D). This requires the use of pseudodifferential operators.
Beurling ultradistributions of Lp-growth
2003
We study the convolutors and the surjective convolution operators acting on spaces of ultradistributions of Lp-growth. In the case p = 2 we obtain complete characterizations. Some results on hypoellipticity are also included. 2003 Elsevier Science (USA). All rights reserved.
Pseudodifferential operators of Beurling type and the wave front set
2008
AbstractWe investigate the action of pseudodifferential operators of Beurling type on the wave front sets. More precisely, we show that these operators are microlocal, that is, preserve or reduce wave front sets. Some consequences on micro-hypoellipticity are derived.