Related papers: On $\star $-Power Conductor domains

This article establishes free versions of two classical theorems: derivatives are curl-free and every curl-free vector field (on a simply connected domain) is a derivative. We show that the derivative of a noncommutative free analytic map…

It has been shown in [Frauenfelder, 2023] that the bounded component of the energy surface of the planer Stark problem after the Levi-Civita transformation are concave toric domains. In this paper, we present a different approach on the…

Polar commutative n-complex numbers of the form u=x_0+h_1x_1+h_2x_2+...+h_{n-1}x_{n-1} are introduced in n dimensions, the variables x_0,...,x_{n-1} being real numbers. The polar n-complex number can be represented, in an even number of…

We give give an elementary and constructive version of the theory of "Pr\"ufer v-Multiplication Domains" (which we call "anneaux \`a diviseurs" in the paper) and Krull Domains. The main results of these theories are revisited from a…

Let D be an integral domain with quotient field K. For any set X, the ring Int(D^X) of integer-valued polynomials on D^X is the set of all polynomials f in K[X] such that f(D^X) is a subset of D. Using the t-closure operation on fractional…

We consider the following question: When are rings of differential operators coherent? If $A$ is a finitely generated smooth domain over a field $k$ of characteristic $0$, then the ring $D$ of differential operators on $A$ is a Noetherian…

Given a commutative Noetherian graded domain $R = \bigoplus_{i\ge 0} R_i$ of dimension $d\geq 2$ with $\dim(R_0) \geq 1$, we prove that any unimodular row of length $d+1$ in $R$ can be completed to the first row of an invertible matrix…

We prove that a non-classical flag domain is pseudoconcave if it satisfies a certain condition on the root system. Moreover, we prove that every point in a one-codimensional real boundary orbit of a non-classical period domains is a…

Using the notion of cyclically pure injective modules, a characterization for rings which are locally valuation is established. As applications, new characterizations for Prufer domains and pure semi-simple rings are provided. Namely, we…

We show that any bounded, simply connected domain with analytic boundary can be realised as a wandering domain of an entire function of any prescribed order in $(0, 1)$. Extending results of Boc Thaler, our construction simultaneously…

We prove Liouville type theorems for $p$-harmonic functions on exterior domains of the $d$-dimensional Euclidean space, where $1<p<\infty$ and $d\geq 2$. We show that every positive $p$-harmonic function satisfying zero Dirichlet, Neumann…

We show that a bounded domain in a Euclidean space is a $W^{1,1}$-extension domain if and only if it is a strong $BV$-extension domain. In the planar case, bounded and strong $BV$-extension domains are shown to be exactly those…

Recursive domain equations have natural solutions. In particular there are domains defined by strictly positive induction. The class of countably based domains gives a computability theory for possibly non-countably based topological…

We derive a closed formula for a star-product on complex projective space and on the domain $SU(n+1)/S(U(1)\times U(n))$ using a completely elementary construction: Starting from the standard star-product of Wick type on $C^{n+1} \setminus…

We consider the spectral structure of the Neumann--Poincar\'e operators defined on the boundaries of thin domains of rectangle shape in two dimensions. We prove that as the aspect ratio of the domains tends to $\infty$, or equivalently, as…

We are going to show that on bounded Lipschitz domain $D$: both $C_{c}^{\infty}(D)$, the set of smooth functions on $D$ with compact support, and $C_{0}^{\infty}(D)$, the set of smooth functions on $D$ with (extension) zero boundary, are…

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…

We shall say that a densely defined closed operator $T$ on a Hilbert space is balanced if $\cD(T)=\cD(T^*)$. Balanced operators are described in terms of their phase operators abnd their moduli. Examples of balanced operators are developed.…

By using a variant Property $(P_q)$ of Catlin, we discuss the relation of small set of weakly pseudoconvex points on the boundary of pseudoconvex domain and compactness of the $\overline{\partial}$-Neumann operator. In particular, we show…

Consider a two-dimensional domain shaped like a wire, not necessarily of uniform cross section. Let $V$ denote an electric potential driven by a voltage drop between the conducting surfaces of the wire. We consider the operator ${\mathcal…