# Some non-analytic-hypoelliptic sums of squares of vector fields

@article{Christ1992SomeNS, title={Some non-analytic-hypoelliptic sums of squares of vector fields}, author={Michael Christ}, journal={Bulletin of the American Mathematical Society}, year={1992}, volume={26}, pages={137-140} }

Certain second-order partial differential operators, which are expressed as sums of squares of real-analytic vector fields in $\Bbb R^3$ and which are well known to be $C^\infty$ hypoelliptic, fail to be analytic hypoelliptic.

## 19 Citations

### Certain sums of Squares of Vector Fields Fail to be Analytic Hypoelliptic

- Mathematics
- 1991

If m {3,4,5,...} then the partial differential operator in R3 fails to be analytic hypoelliptic. This results from the existence of parameters C such that the ordinary differential equation has a…

### A family of degenerate differential operators

- Mathematics
- 1993

Certain second-order partial differential operators, expressed as sums of squares of complex vector fields, are shown not to beC∞ hypoelliptic even at a point, rather than merely in an open set. The…

### Semiclassical analysis of a nonlinear eigenvalue problem and nonanalytic hypoellipticity

- Mathematics
- 2003

A semiclassical analysis of a nonlinear eigenvalue problem arising from the study of the failure of analytic hypoellipticity is given. A general family of hypoelliptic, but not analytic hypoelliptic…

### On the Singularities of Non-Analytic Szego Kernels

- Mathematics
- 1999

The CR manifold Mm = {(z1 ,z 2) ∈ C 2 ; � z2 = (� z1) 2m }(m =2 , 3 ,... ) is a counterexample, which was given by Christ and Geller, to analytic hypoellipticity of ¯ ∂b and real analyticity of the…

### Existence of solution for some quasi-homogenous and quasi-elliptic Nonlinear Eigenvalue Problems

- MathematicsZANCO JOURNAL OF PURE AND APPLIED SCIENCES
- 2019

The existence of solutions for a non linear eigenvalue problems is well studied and proved for n even. In this article we will study the case of odd dimension n>1 for the family of quasi-homogeneous…

### Non linear eigenvalue problems

- Mathematics
- 2004

In this paper we consider generalized eigenvalue problems for a family of operators with a polynomial dependence on a complex parameter. This problem is equivalent to a genuine non self-adjoint…

### Breakdown of Analyticity for ¯ ∂ B and Szegö Kernels

- Mathematics
- 1996

The CR manifold M m = {Imz 2 = [Rez 1 ] 2m }(m = 2, 3,. . .) is the counterexample, which has been given by M. Christ and D. Geller, to analytic hypoellipticity of ¯ ∂ b and real analyticity of the…

### Breakdown of analyticity for d-bar-b and Szego kernels

- Mathematics
- 1996

The CR manifold M_m = { Im z_2= Re z_1^{2m} } (m=2,3,...) is the counterexample, which has been given by M. Christ and D. Geller, to analytic hypoellipticity of d-bar-b and real analyticity of the…

### A Necessary Condition For Analytic Hypoellipticity

- Mathematics
- 1994

A partial differential operator, L, is said to be analytic hypoelliptic in some open set Ω, if for every open U ⊂ Ω and every distribution u ∈ D′(U), if Lu ∈ C(U), then u ∈ C(U). Let X1, X2 be real…

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If m {3,4,5,...} then the partial differential operator in R3 fails to be analytic hypoelliptic. This results from the existence of parameters C such that the ordinary differential equation has a…

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