Related papers: Effective Kohn Algorithm for Special Domain Define…

We prove local hypoellipticity of the complex Laplacian $\Box$ and of the Kohn Laplacian $\Box_b$ in a pseudoconvex boundary when, for a system of cut-off $\eta$, the gradient $\partial_b\eta$ and the Levi form…

Let D be a bounded domain in n-dimensional Eucledian space with a smooth boundary. We indicate appropriate Sobolev spaces of negative smoothness to study the non-homogeneous Cauchy problem for an elliptic differential complex {A_i} of first…

It is an observation due to J.J. Kohn that for a smooth bounded pseudoconvex domain D in $C^n$ there exists s>0 such that the dbar-Neumann operator on D maps $W^s_{(0,1)}(D)$ (the space of $(0,1)$-forms with coefficient functions in…

This paper treats subelliptic estimates for the $\bar{\partial}$-Neumann problem on a class of domains known as regular coordinate domains. Our main result is that the largest subelliptic gain for a regular coordinate domain is bounded…

The $k$-Cauchy-Fueter operators and complexes are quaternionic counterparts of the Cauchy-Riemann operator and the Dolbeault complex in the theory of several complex variables. To develop the function theory of several quaternionic…

We give a new complexity bound for calculating the complex dimension of an algebraic set. Our algorithm is completely deterministic and approaches the best recent randomized complexity bounds. We also present some new, significantly sharper…

To simulate plasma phenomena, large-scale computational resources have been employed in developing high-precision and high-resolution plasma simulations. One of the main obstacles in plasma simulations is the requirement of computational…

An important problem in applications is the approximation of a function $f$ from a finite set of randomly scattered data $f(x_j)$. A common and powerful approach is to construct a trigonometric least squares approximation based on the set…

We consider the Schur-Horn problem for normal operators in von Neumann algebras, which is the problem of characterizing the possible diagonal values of a given normal operator based on its spectral data. For normal matrices, this problem is…

Explicit expressions are given for the actions and radial matrix elements of basic radial observables on multi-dimensional spaces in a continuous sequence of orthonormal bases for unitary SU(1,1) irreps. Explicit expressions are also given…

By considering intrinsic geometric conditions, we introduce a new class of domains in complex Euclidean space. This class is invariant under biholomorphism and includes strongly pseudoconvex domains, finite type domains in dimension two,…

Let $\Omega$ be an open, simply connected, and bounded region in $\mathbb{R}^{d}$, $d\geq2$, and assume its boundary $\partial\Omega$ is smooth. Consider solving an elliptic partial differential equation $-\Delta u+\gamma u=f$ over $\Omega$…

We discuss the wellposedness of the Neumann problem on a half-space for the Kohn-Laplacian in the Heisenberg group. We then construct the Neumann function and explicitly represent the solution of the associated inhomogeneous problem.

For a sum of squares domain of finite D'Angelo 1-type at the origin, we show that the polynomial model obtained from the computation of the Catlin multitype at the origin of such a domain is likewise a sum of squares domain. We also prove,…

In this work, we present scalable balancing domain decomposition by constraints methods for linear systems arising from arbitrary order edge finite element discretizations of multi-material and heterogeneous 3D problems. In order to enforce…

In the convergence analysis of numerical methods for solving partial differential equations (such as finite element methods) one arrives at certain generalized eigenvalue problems, whose maximal eigenvalues need to be estimated as…

We consider radial complex scaling/perfectly matched layer methods for scalar resonance problems in homogeneous exterior domains. We introduce a new abstract framework to analyze the convergence of domain truncations and discretizations.…

We examine the use of the Dirichlet-to-Neumann coarse space within an additive Schwarz method to solve the Helmholtz equation in 2D. In particular, we focus on the selection of how many eigenfunctions should go into the coarse space. We…

The theory of abstract Friedrichs operators, introduced by Ern, Guermond and Caplain (2007), proved to be a successful setting for studying positive symmetric systems of first order partial differential equations (Friedrichs, 1958),…

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…