Related papers: Denjoy-Carleman Microlocal Regularity on Smooth Re…
In this paper we obtain a Carleman approximation theorem for maps from Stein manifolds to Oka manifolds. More precisely, we show that under suitable complex analytic conditions on a totally real set $ M $ of a Stein manifold $X$, every…
A systematic geometric theory for the ultradifferentiable (non-quasianalytic and quasianalytic) wavefront set similar to the well-known theory in the classic smooth and analytic setting is developed. In particular an analogue of Bony's…
In this work we consider a question in the calculus of variations motivated by riemannian geometry, the isoperimetric problem. We show that solutions to the isoperimetric problem, close in the flat norm to a smooth submanifold, are…
We approximate smooth maps defined on non-compact totally real manifolds by holomorphic automorphisms of $\mathbb C^n$.
We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for…
We deal with the electromagnetic waves propagation in the harmonic regime. We derive the Foldy-Lax approximation of the scattered fields generated by a cluster of small conductive inhomogeneities arbitrarily distributed in a bounded domain…
In this article the notion of ultradifferentiable CR manifold is introduced and an ultradifferentiable regularity result for finitely nondegenerate CR mappings is proven. Here ultradifferentiable means with respect to Denjoy-Carleman…
In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…
A controlled sweeping process with prox-regular set, $W^{1,2}$-controls, and separable endpoints constraints is considered in this paper. Existence of optimal solutions is established and local optimality conditions are derived via strong…
We show that a version of the desingularization theorem of Hironaka holds for certain classes of infinitely differentiable functions (essentially, for subrings that exclude flat functions and are closed under differentiation and the…
We establish elliptic regularity for nonlinear inhomogeneous Cauchy-Riemann equations under minimal assumptions, and give a counterexample in a borderline case. In some cases where the inhomogeneous term has a separable factorization, the…
We continue the development, by reduction to a first order system for the conormal gradient, of $L^2$ \textit{a priori} estimates and solvability for boundary value problems of Dirichlet, regularity, Neumann type for divergence form second…
This paper presents an averaging method for nonlinear systems defined on Riemannian manifolds. We extend closeness of solutions results for ordinary differential equations on $R^{n}$ to dynamical systems defined on Riemannian manifolds by…
We study continuous approximate solutions to polynomial equations over the ring $C(X)$ of continuous complex-valued functions over a compact Hausdorff space $X$. We show that when $X$ is one-dimensional, the existence of such approximate…
Optimization on Riemannian manifolds widely arises in eigenvalue computation, density functional theory, Bose-Einstein condensates, low rank nearest correlation, image registration, and signal processing, etc. We propose an adaptive…
This paper focuses on minimizing a smooth function combined with a nonsmooth regularization term on a compact Riemannian submanifold embedded in the Euclidean space under a decentralized setting. Typically, there are two types of approaches…
We consider minimization of functions that are compositions of convex or prox-regular functions (possibly extended-valued) with smooth vector functions. A wide variety of important optimization problems fall into this framework. We describe…
In this paper we consider the non-cutoff Boltzmann equation in spatially inhomogeneous case. We prove the propagation of Gevrey regularity for the so-called smooth Maxwellian decay solutions to the Cauchy problem of spatially inhomogeneous…
This study presents a method for constructing a sequence of approximate solutions of increasing accuracy to general equilibrium models on nonlocal domains. The method is based on a technique originated from dynamical systems theory. The…
In this paper we study the long time behavior for a semilinear wave equation with space-dependent and nonlinear damping term. After rewriting the equation as a first order system, we define a class of approximate solutions that employ…