Related papers: Differential Operators on Modular Extensions
We give a sufficient condition for a bi-invariant weight on a Frobenius bimodule to satisfy the extension property. This condition applies to bi-invariant weights on a finite Frobenius ring as a special case. The complex-valued functions on…
Using polynomial evaluation, we give some useful criteria to answer questions about divisibility of polynomials. This allows us to develop interesting results concerning the prime elements in the domain of coefficients. In particular, it is…
In this paper we give some sufficient conditions of analyticity and univalence for functions defined by an integral operator. Next, we refine the result to a quasiconformal extension criterion with the help of the Becker's method. Further,…
A necessary condition and a sufficient condition for one weight norm inequalities on Morrey spaces to hold are given for the fractional maximal operator and the fractional integral operator. We clarify the difference between the behavior of…
We show that any finite set of linear partial differential operators with continuous coefficients is linearly dependent if and only if it is locally linearly dependent. It follows that the reflexive closure of any finite set of such…
Given a differential operator defined in terms of left-invariant vector fields on a Lie group, we prove that the local condition defining maximal hypoellipticity is equivalent to a global estimate if the operator is left invariant. As a…
We provide Fredholm conditions for compatible differential operators on certain Lie manifolds (that is, on certain possibly non-compact manifolds with nice ends). We discuss in more detail the case of manifolds with cylindrical, hyperbolic,…
In the present paper we continue the project of systematic construction of invariant differential operators on the example of the non-compact exceptional Lie algebra $F"_4$ which is the split rank one form of the exceptional Lie algebra…
We present new examples of complexes of differential operators of order $k$ (any given positive integer) that satisfy div-curl and/or $L^1$-duality estimates.
We determine the dual modules of all irreducible modules of alternating groups over fields of characteristic 2.
In this paper, we characterize complementable operators and provide more precise expressions for the Schur complement of these operators using a single Douglas solution. We demonstrate the existence of subspaces where the given operator is…
Abstract approaches to maximum and anti-maximum principles for differential operators typically rely on the condition that all vectors in the domain of the operator are dominated by the leading eigenfunction of the operator. We study the…
We examine algebraic conditions for the sectional positivity of the Riemann curvature operator. We describe sufficient conditions for dimension $n=4$, and complete characterization for a dense open subset of the space of operators in…
In this article, we explore the problem of constructing high-dimensional expanders through the study of relations between expansion constants over different rings. We investigate expansion constants of integer matrices regarded as morphisms…
While the asymptotic Borel mapping, sending a function into its series of asymptotic expansion in a sector, is known to be surjective for arbitrary openings in the framework of ultraholomorphic classes associated with sequences of rapid…
For a large class of integral operators or second order differential operators, their isospectral (or cospectral) operators are constructed explicitly in terms of $h$-transform (duality). This provides us a simple way to extend the known…
Let k be a field, let R be a ring of polynomials in a finite number of variables over k, let D be the ring of k-linear differential operators of R and let f be a non-zero element of R. It is well-known that R_f, with its natural D-module…
We provide a numerical method to determine the critical lengths of linear differential operators with constant real coefficients. The need for such a procedure arises when the orders increase. The interest of this article is clearly on the…
Let $r$ be a positive integer, $N$ be a nonnegative integer and $\Omega \subset \mathbb{R}^{r}$ be a domain. Further, for all multi-indices $\alpha \in \mathbb{N}^{r}$, $|\alpha|\leq N$, let us consider the partial differential operator…
The ring of integers and the discriminant are determined for number fields which are simple radical extensions.