Related papers: Analyticity and loss of derivatives

We present a general algorithm to show that a scattering operator associated to a semilinear dispersive equation is real analytic, and to compute the coefficients of its Taylor series at any point. We illustrate this method in the case of…

Analytic versions of QCD are those whose coupling alpha_s(Q^2) does not have the unphysical Landau singularities on the space-like axis (-q^2=Q^2 > 0). The coupling is analytic in the entire complex plane except the time-like axis (Q^2 <…

Let $-\im\Lie_\T$ (essentially Lie derivative with respect to $\T$, a smooth nowhere zero real vector field) and $P$ be commuting differential operators, respectively of orders 1 and $m\geq 1$, the latter formally normal, both acting on…

It was recently shown in [4] that, for $L_2$-approximation of functions from a Hilbert space, function values are almost as powerful as arbitrary linear information, if the approximation numbers are square-summable. That is, we showed that…

For a projective algebraic variety $V$ with isolated singularities, endowed with a metric induced from an embedding, we consider the analysis of the natural partial differential operators on the regular part of $V$. We show that, in the…

The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…

In this paper we provide a framework for quantitative statements on distances and measures when studying algebraic varieties and morphisms of algebraic varieties over local fields. We will concentrate on local fields of the type…

This study is an attempt at generalizing the class of partially hypoelliptic differential operators to a class of pseudodifferential operators, Symbol ideals are formed on the set of lineality and we discuss suitable topologies that allow…

Let $A$ be a standard graded $\mathbb{K}$-algebra of finite type over an algebraically closed field of characteristic zero. We use apolarity to construct, for each degree $k$, a projective variety whose osculating defect in degree $s$ is…

We consider a Froeschl\'e map and we add a weak dissipation of the form $\lambda(\varepsilon) = 1- \varepsilon^3$, where $\varepsilon$ is the parameter of perturbation. We compute formal expansions of lower dimensional tori, both in the…

Smooth hypoellipticity for scalar equations is quite well understood presently. On the other hand, much remains to be done for systems and/or at different levels of regularity and in particular for $L^1$-hypoellipticity. In this article we…

We establish new results on weighted $L^2$ extension of holomorphic top forms with values in a holomorphic line bundle, from a smooth hypersurface cut out by a holomorphic function. The weights we use are determined by certain functions…

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of…

In 1979 J.J. Kohn gave an indirect argument via the Diederich-Forn\ae ss Theorem showing that finite D'Angelo type implies termination of the Kohn algorithm for a pseudoconvex domain with real-analytic boundary. We give here a direct…

In this work, we explore an extension of Hilbert series techniques to count operators that include derivatives. For sufficiently low-derivative operators, we find an algorithm that gives the number of invariant operators, properly…

The Helmholtz decomposition splits a sufficiently smooth vector field into a gradient field and a divergence-free rotation field. Existing decomposition methods impose constraints on the behavior of vector fields at infinity and require…

We define a reduction covariant for the representations a la Vinberg associated to stably graded Lie algebras. We then give an analogue of the LLL algorithm for the odd split special orthogonal group and show how this can be combined with…

Helmholtz decomposition theorem for vector fields is presented usually with too strong restrictions on the fields. Based on the work of Blumenthal of 1905 it is shown that the decomposition of vector fields is not only possible for…

Given a finite collection of $C^1$ vector fields on a $C^2$ manifold which span the tangent space at every point, we consider the question of when there is locally a coordinate system in which these vector fields are real analytic. We give…

For a class of non-selfadjoint semiclassical pseudodifferential operators with double characteristics, we study bounds for resolvents and estimates for low lying eigenvalues. Specifically, assuming that the quadratic approximations of the…