David S. Tartakoff

On the global real analyticity of solutions to the neumann problems

(1976). On the global real analyticity of solutions to the neumann problems. Communications in Partial Differential Equations: Vol. 1, No. 5, pp. 401-435.

Propagation of Gevrey Regularity for a Class of Hypoelliptic Equations

We prove results on the propagation of Gevrey and analytic wave front sets for a class of

Microlocal analyticity for the canonical solution to on Some Rigid Weakly Pseudoconvex Hypersurfaces in C2

C^\infty

Analyticity for singular sums of squares of degenerate vector fields

hypoelliptic equations with double characteristics.

Gevrey Hypoellipticity for an Interesting Variant of Kohn’s Operator

In a recent paper we proved first global analyticity for the canonical solution to on weakly pseudoconvex (rigid) CR manifolds in C2 when the range of was closed ([8]) and subsequently the microlocal real analytic regularity on strictly pseudoconvex domains in C2 ([10]). Here we prove the microlocal real analytic regularity near 0 of the canonical solution to on compact hypersurfaces in C2 which, near 0, are of the form h(s)≥0,h not identically equal to 0. We remark that microlocalization is necessary even for the global result in C2

A class of sums of squares with a given Poisson-Treves stratification

Recently J. J. Kohn (2005) proved C ∞ hypoellipticity for P k = LL + L|z| 2k L = -L*L-(z k L)* -k z L with L = ∂ ∂z + iz∂ ∂t, (the negative of) a singular sum of squares of complex vector fields on the complex Heisenberg group, an operator which exhibits a loss of k - 1 derivatives. Subsequently, M. Derridj and D. S. Tartakoff proved analytic hypoellipticity for this operator using rather different methods going back to earlier methods of Tartakoff. Those methods also provide an alternate proof of the hypoellipticity given by Kohn. In this paper, we consider the equation P m,k = L m L m + L m |z| 2k L m with L m = ∂ ∂z + iz|z| 2m ∂ ∂t, for which the underlying manifold is only of finite type, and prove analytic hypoellipticity using methods of Derridj and Tartakoff. This operator is also subelliptic with large loss of derivatives, but the exact loss plays no role for analytic hypoellipticity. Nonetheless, these methods give a proof of C ∞ hypoellipticity with precise loss as well, which is to appear in a forthcoming paper by A. Bove, M. Derridj, J. J. Kohn and the author.

Gevrey and Analytic Hypoellipticity

In this paper we consider the analogue of Kohn’s operator but with a point singularity,

Analytic Hypoellipticity for a Sum of Squares of Vector Fields in ℝ3 Whose Poisson Stratification Consists of a Single Symplectic Stratum of Codimension Four

P = BB^* + B^* (t^{2\ell } + x^{2k} )B, B = D_x + ix^{q - 1} D_t .