arXiv math/05035062005-03-23math.CVmath.AP

A remark on sums of squares of complex vector fields

Michael Christ

备注：: 5 pages

英文摘要：

This note is a comment on a recent paper by J. J. Kohn. We give an example of a second order partial differential operator, expressed as a sum of squares of complex vector fields satisfying the bracket condition, that is not hypoelliptic.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

阅读原文

阅读 PDF ↗

arXiv 页面 ↗HTML 原文 ↗

本文内容

英文摘要相关论文

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

继续探索

相关论文

Singular Sums of Squares of Degenerate Vector Fields

We simplify and give an alternative proof of hypoellipticity for generalizations of the singular sum of squares of complex vector fields studied by Kohn, with an appendix by Derridj and Tartakoff, in the Annals of Mathematics, vol. 162 no. 2, 2005, pp. 943-986. The main generalization is that the complex vector fields now come from domains of finite type. We also prove real analytic hypoellipticity and the optimality of our estimates.

2006-01-22math.APmath.CV

Global Analytic Hypoellipticity for a Class of Quasilinear Sums of Squares of Vector Fields

A global real analytic regularity theorem for a quasilinear sum of squares of vector fields of Hormander rank 2 is given. A related local result for a special case was proved recently by the second author and L. Zanghirati in a paper titled "Local Real Analyticity of Solutions for sums of squares of non-linear vector fields".

2003-09-30math.APmath.CVmath.SG

Loss of derivatives for systems of complex vector fields and sums of squares

We discuss, both for systems of complex vector fields and for sums of squares, the phenomenon discovered by Kohn of hypoellipticity with loss of derivatives.

2010-09-02math.CV

Holomorphic Rational Functions of Several Variables and Sums of Squares of Polynomials

Necessary and sufficient conditions are obtained under which the numerator of the partial derivative of a rational function holomorphic in open upper poly-halfplane is the sum of squares of polynomials.

2021-06-30math.CV

Complete Monotonicity and Zeros of Sums of Squared Baskakov Functions

We prove complete monotonicity of sums of squares of generalized Baskakov basis functions by deriving the corresponding results for hypergeometric functions. Moreover, in the central Baskakov case we study the distribution of the complex zeros for large values of a parameter. We finally discuss the extension of some results for sums of higher powers.

2014-11-28math.CAmath.CV

Sums of squares in pseudoconvex hypersurfaces and torsion phenomena for Catlin's boundary systems

Given a pseudoconvex hypersurface in C^n and an arbitrary weight, we show the existence of local coordinates in which the polynomial model contains a particularly simple sum of squares of monomials. Our second main result provides a normalization of a part of any Catlin boundary system. We illustrate by an example that this normalization cannot be extended to the rest of the boundary system due to the existence of what we refer to as torsion.

2018-06-04math.CV