Results 101 to 110 of about 51,079 (125)
Some of the next articles are maybe not open access.
Wave Front Set of Solutions to Sums of Squares of Vector Fields
Memoirs of the American Mathematical Society, 2012We study the (micro)hypoanalyticity and the Gevrey hypoellipticity of sums of squares of vector fields in terms of the Poisson-Treves stratification. The FBI transform is used. We prove hypoanalyticity for several classes of sums of squares and show that our method, though not general, includes almost every known hypoanalyticity result.
ALBANO, PAOLO, BOVE, ANTONIO
openaire +2 more sources
General Sums of Squares of Real Vector Fields
2011The Laplacian $$\Delta ={ \sum \nolimits }_{1}^{n} \frac{{\partial }^{2}} {\partial {x}_{j}^{2}}$$ and the partial Laplacian $$\Delta ' ={ \sum \nolimits }_{1}^{n'
openaire +1 more source
Fundamental solutions for sum of squares of vector fields operators with C1,α coefficients
Forum Mathematicum, 2012Consider in \(\mathbb{R}^n_x\) the sum-of-squares \(L=\sum_{j=1}^mX_j^2\), \(1\leq m\leq n\), where the locally Euclidean Lipschitz continuous vector fields \(X_j\) have the form \[ X_j=\frac{\partial}{\partial x_j}+\sum_{k=m+1}^na_{jk}(x)\frac{\partial}{\partial x_k},\,\,\,\,1\leq j\leq m, \] and satisfy the step-two condition \[ \frac{\partial ...
openaire +2 more sources
Stability Analysis of Hybrid Automata with Set-Valued Vector Fields Using Sums of Squares
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2006Stability analysis is one of the most important problems in analysis of hybrid dynamical systems. In this paper, a computational method of Lyapunov functions is proposed for stability analysis of hybrid automata that have set-valued vector fields. For this purpose, a formulation of matrix-valued sums of squares is provided and applied to derive an LMI ...
I. MASUBUCHI, T. TSUJI
openaire +1 more source
Journal of Geometric Analysis, 2008
The purpose of this paper is to study analytic hypoellipticity for certain sums of squares of vector fields having non-trivial Poisson-Treves stratification, i.e., the stratification has non-trivial strata at depth larger than one. In all examples known so far, analytic hypoellipticity holds in the sense of germs when the characteristic manifold is non-
BOVE, ANTONIO, D. S. Tartakoff
openaire +1 more source
The purpose of this paper is to study analytic hypoellipticity for certain sums of squares of vector fields having non-trivial Poisson-Treves stratification, i.e., the stratification has non-trivial strata at depth larger than one. In all examples known so far, analytic hypoellipticity holds in the sense of germs when the characteristic manifold is non-
BOVE, ANTONIO, D. S. Tartakoff
openaire +1 more source
Certain sums of Squares of Vector Fields Fail to be Analytic Hypoelliptic
Communications in Partial Differential Equations, 1991If 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 nontrivial solution which remains bounded ...
openaire +1 more source
On the analyticity of solutions of sums of squares of vector fields
2006The note describes, in simple analytic and geometric terms, the global Poisson stratification of the characteristic variety Char L of a second-order linear differential operator −L = X 1 2 + ... + X r 2 , i.e., a sum-of-squares of real-analytic, real vector fields X i on an analytic manifold Ω.
openaire +1 more source
Gevrey Hypo-ellipticity for Sums of Squares of Vector Fields: some examples
2005The Gevrey hypo-ellipticity of a couple of model operators is studied in detail. We match the obtained Gevrey regularity against the structure of the Poisson-Treves stratification of the operators.
openaire +1 more source
2009
We prove analytic hypoellipticity for a sum of squares of vector fields in ℝ3 all of whose Poisson strata are equal and symplectic of codimension four, extending in a model setting the recent general result of Cordaro and Hanges in codimension two [2].
openaire +1 more source
We prove analytic hypoellipticity for a sum of squares of vector fields in ℝ3 all of whose Poisson strata are equal and symplectic of codimension four, extending in a model setting the recent general result of Cordaro and Hanges in codimension two [2].
openaire +1 more source
Duals of Cesàro sequence vector lattices, Cesàro sums of Banach lattices, and their finite elements
Archiv Der Mathematik, 2023Martin R. Weber
exaly