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pro vyhledávání: '"Tartakoff, David S."'
Autor:
Tartakoff, David S.
We study the regularity of Gevrey vectors for H\"ormander operators $$ P = \sum_{j=1}^m X_j^2 + X_0 + c$$ where the $X_j$ are real vector fields and $c(x)$ is a smooth function, all in Gevrey class $G^{s}.$ The principal hypothesis is that $P$ satisf
Externí odkaz:
http://arxiv.org/abs/1708.02978
Autor:
Tartakoff, David S.
Publikováno v:
Far East J. Appl. Math. 15 (2004), no. 3, 353--363
In an interesting note, E.M. Stein observed some 20 years ago that while the Kohn Laplacian $\square_b$ on functions is neither locally solvable nor (analytic) hypoelliptic, the addition of a non-zero complex constant reversed these conclusions at le
Externí odkaz:
http://arxiv.org/abs/math/0609804
Autor:
Bove, Antonio, Tartakoff, David S.
Publikováno v:
J. Geom. Anal. 13 (2003), no. 3, 391--420
We study a class of sum of squares exhibiting the same Poisson-Treves stratification as the Oleinik-Radkevi\v{c} operator. We find three types of operators having distinct microlocal structures. For one of these we prove a Gevrey hypoellipticity theo
Externí odkaz:
http://arxiv.org/abs/math/0609803
Autor:
Bove, Antonio, Tartakoff, David S.
We consider an operator $ P $ which is a sum of squares of vector fields with analytic coefficients. The operator has a non-symplectic characteristic manifold, but the rank of the symplectic form $ \sigma $ is not constant on $ \Char P $. Moreover th
Externí odkaz:
http://arxiv.org/abs/math/0609777
Autor:
Tartakoff, David S.
We present an elementary, $L^2,$ proof of Fedi\u{\i}'s theorem on arbitrary (e.g., infinite order) degeneracy and extensions. In particular, the proof allows and shows $C^\infty,$ Gevrey, and real analytic hypoellipticity, and allows the coefficents
Externí odkaz:
http://arxiv.org/abs/math/0609778
We consider a second order operator with analytic coefficients whose principal symbol vanishes exactly to order two on a symplectic real analytic manifold. We assume that the first (non degenerate) eigenvalue vanishes on a symplectic submanifold of t
Externí odkaz:
http://arxiv.org/abs/math/0603317
Publikováno v:
Annals of Mathematics vol. 162 no. 2, September 2005, pp. 943-986
For each value of k, two complex vector fields satisfying the bracket condition are exhibited the sum of whose squares is hypoelliptic but not subelliptic - in fact the operator loses k-1 derivatives in Sobolev norms. In the Appendix it is proven tha
Externí odkaz:
http://arxiv.org/abs/math/0601646
Publikováno v:
Mathematical Research Letters {\bf 13} (5), (2006), pp.~683-702.
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, p
Externí odkaz:
http://arxiv.org/abs/math/0601523
Autor:
Tartakoff, David S.
Publikováno v:
Proc. Amer. Math. Soc. {\bf 134}, (2006), pp.~3343-3352.
In this paper we prove local analytic hypoellipticity for a degenerate sum of squares of complex vector fields generalizing those of Kohn in "Hypoellipticity and Loss of Derivatives". Kohn's article is to appear in the Annals of Mathematics with an a
Externí odkaz:
http://arxiv.org/abs/math/0505650