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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'
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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.
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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 ...
Izumi Masubuchi, Tokihisa Tsuji
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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
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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
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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 ...
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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 ...
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On a class of sums of squares related to Hamiltonians with a non periodic magnetic field
Journal of Mathematical Analysis and Applications, 2023Antonio Bove +2 more
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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].
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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].
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Analytic regularity for solutions to sums of squares: an assessment
Complex Analysis and Its Synergies, 2020Antonio Bove +2 more
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Symmetric Non-Negative Forms and Sums of Squares
Discrete and Computational Geometry, 2020Grigoriy Blekherman +2 more
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