A Necessary Condition For Analytic Hypoellipticity

A Necessary Condition for Weyl-Heisenberg Frames

Analytic Hypoellipticity in Dimension Two

A simple geometric condition is sufficient for analytic hypoellipticity of sums of squares of two vector fields in R. This condition is proved to be necessary for generic vector fields and for various special cases, and to be both necessary and sufficient for a closely related family of operators.

Nonlinear eigenvalues and analytic hypoellipticity

Motivated by the problem of analytic hypoellipticity, we show that a special family of compact non selfadjoint operators has a non zero eigenvalue. We recover old results obtained by ordinary differential equations techniques and show how it can be applied to the higher dimensional case. This gives in particular a new class of hypoelliptic, but not analytic hypoelliptic operators.

Local Gevrey and Quasi - Analytic Hypoellipticity For

Introduction. The db complex is well defined on any smooth CR manifold M, and once a metric is fixed, so is the complex Laplace-Beltrami operator Db on forms of type (p, q). For compact M without boundary, the bb cohomology of M may be studied via Ub [6], and thus local smoothness of solutions to Dbu = ƒ is important. In its own right, Ub is a prototype of doubly characteristic operators. Under...

A necessary condition for multiple objective fractional programming

In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.