Related papers: The inhomogeneous Cauchy-Riemann equation for weig…

We investigate integral representation of vector-valued function spaces, i.e., of subspaces $H\subset C(K,E)$, where $K$ is a compact space and $E$ is a (real or complex) Banach space. We point out that there are two possible ways of…

We introduce a vector-valued version of a uniform algebra, called the vector-valued function space over a uniform algebra. The diameter two properties of the vector-valued function space over a uniform algebra on an infinite compact…

Let $X$ be a compact Hausdorff space, let $E$ be a Banach space, and let $C(X,E)$ stand for the Banach space of $E$-valued continuous functions on $X$ under the uniform norm. In this paper we characterize Integral operators (in the sense of…

We prove that any compact Cauchy horizon with constant non-zero surface gravity in a smooth vacuum spacetime is a smooth Killing horizon. The novelty here is that the Killing vector field is shown to exist on both sides of the horizon. This…

We prove that an integral Cauchy-Riemann inequality holds for any pair of smooth functions $(f,h)$ on the 2-sphere $\mathbb{S}^2$, and equality holds iff $f$ and $h$ are related $\lambda_1$-eigenfunctions. We extend such inequality to…

In this paper, we study vector valued de Branges spaces associated with a de Branges operator, defined as a pair of Fredholm operator valued analytic functions on a domain symmetric with respect to the unit circle. Using a suitable direct…

Let E be a separable (or the dual of a separable) symmetric function space, let M be a semifinite von Neumann algebra and let E(M) be the associated noncommutative function space. Let $(\epsilon_k)_k$ be a Rademacher sequence, on some…

A Cauchy type integral operator is associated to a class of integrable vector fields with complex coefficients. Properties of the integral operator are used to deduce Holder solvability of semilinear equations and a strong similarity…

We associate a weight function to pairs consisting of a smooth and proper variety X over a complete discretely valued field and a differential form on X of maximal degree. This weight function is a real-valued function on the…

We prove an implicit function theorem for Keller C^k_c-maps from arbitrary real or complex topological vector spaces to Frechet spaces, imposing only a certain metric estimate on the partial differentials. As a tool, we show the…

The study presents a vector-valued extension of the classical Mercer theorem within the framework of reproducing kernel Hilbert spaces defined over Kaplansky-Hilbert modules associated with the algebra of essentially bounded measurable…

We prove functional inequalities on vector fields on the Euclidean space when it is equipped with a bounded measure that satisfies a Poincar\'e inequality, and study associated self-adjoint operators. The weighted Korn inequality compares…

We prove upper pointwise estimates for the Bergman kernel of the weighted Fock space of entire functions in $L^2(e^{-2\phi})$ where $\phi$ is a subharmonic function with $\Delta \phi$ a doubling measure. We derive estimates for the…

In this paper, we have considered vector valued reproducing kernel Hilbert spaces (RKHS) $\mathcal{H}$ of entire functions associated with operator valued kernel functions. de Branges operators $\mathfrak{E}=(E_- , E_+)$ analogous to de…

We describe the strong dual space $({\mathcal O} (D))^*$ for the space ${\mathcal O} (D)$ of holomorphic functions of several complex variables over a bounded Lipschitz domain $D$ with connected boundary $\partial D$ (as usual, ${\mathcal…

The main purpose of this paper is to study the validity of the Hausdorff-Young inequality for vector-valued functions defined on a non-commutative compact group. The natural context for this research is that of operator spaces. This leads…

Let Vect(R) be the Lie algebra of smooth vector fields on R. The space of symbols Pol(T^* R) admits a non-trivial deformation (given by differential operators on weighted densities) as a Vect(R)-module that becomes trivial once the action…

Motivated by problems in which data are given over covering generating families, we suggest a new cohomology theory for diffeological spaces, called diffeological \v{C}ech cohomology, which is an exact $ \partial $-functor of the section…

We discuss linear algebra of infinite-dimensional vector spaces in terms of algebraic (Hamel) bases. As an application we prove the surjectivity of a large class of linear partial differential operators with smooth ($\mathcal…

The notion of projection families generalizes the classical notions of vector- and operator-valued measures. We show that projection families are general enough to extend the Spectral Theorem to Banach algebras and operators between Banach…