Related papers: Wolff's Theorem on Ideals for Matrices

A waveguide coincides with a three-dimensional domain G having finitely many cylindrical outlets to infinity; the boundary of G is smooth. In G, we consider the stationary Maxwell system with real spectral parameter k and identity matrices…

There are several remarks on Hilbert series of finitely presented (f. p.) associative algebras over a field and their modules. First, given an integer $D$, the set of Hilbert series of right-sided ideals with generators and relations of…

We consider Diophantine inequalities of the kind |f(x)| \le m, where F(X) \in Z[X] is a homogeneous polynomial which can be expressed as a product of d homogeneous linear forms in n variables with complex coefficients and m\ge 1. We say…

We introduce a topology on the ideal space of inductive limits of C*-algebras built by a topological inverse limit of the Fell topologies on the C*-algebras of the given inductive sequence and we produce conditions for when this topology…

We provide a new proof of ``most" cases of the polynomial Wiener-Wintner theorem for $\sigma$-finite spaces, using hard-analytic methods. Specifically, we prove that whenever $(X,\mu,T)$ is a $\sigma$-finite measure-preserving system, and…

In this paper, we draw a connection between ideal lattices and Gr\"{o}bner bases in the multivariate polynomial rings over integers. We study extension of ideal lattices in $\mathbb{Z}[x]/\langle f \rangle$ (Lyubashevsky \& Micciancio,…

The Schur-Horn theorem is a classical result in matrix analysis which characterizes the existence of positive semidefinite matrices with a given diagonal and spectrum. In recent years, this theorem has been used to characterize the…

The main result of the paper is the following generalization of Forelli's theorem: Suppose F is a holomorphic vector field with singular point at p, such that F is linearizable at p and the matrix is diagonalizable with the eigenvalues…

Let $\fa$ be an ideal of a local ring $(R,\fm)$ and $X$ a $d$-dimensional homologically bounded complex of $R$-modules whose all homology modules are finitely generated. We show that $H^d_{\fa}(X)=0$ if and only if $\dim \hat{R}/\fa…

Suppose $R$ is a $\mathbb{Q}$-Gorenstein $F$-finite and $F$-pure ring of prime characteristic $p>0$. We show that if $I\subseteq R$ is a compatible ideal (with all $p^{-e}$-linear maps) then there exists a module finite extension $R\to S$…

This article is devoted to the study of solutions of non-homogenous linear differential equations having entire coefficients. We get all non-trivial solutions of infinite order of equation $f^{(n)}+a_{n-1}(z)f^{(n-1)}+\ldots…

We extend Theorem 1 of R. Reams, A Galois approach to m-th roots of matrices with rational entries, LAA 258 (1997), 187-194. Let $p(\lambda)$ be any polynomial over $\mathbb{Q}$ and let $A\in M_n(\mathbb{Q})$ have irreducible characteristic…

Polar decompositions of quaternion matrices with respect to a given indefinite inner product are studied. Necessary and sufficient conditions for the existence of an $H$-polar decomposition are found. In the process an equivalent to Witt's…

The purpose of this paper is to study the properties of the solutions to the biharmonic equations: $\Delta(\Delta f)=g$, where $g:$ $\overline{\mathbb{D}}\rightarrow\mathbb{C}$ is a continuous function and $\overline{\mathbb{D}}$ denotes…

Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…

In this article, we extend the notion of the $F$-thresholds of ideals to the $F$-thresholds for filtrations of ideals. The existence of $F$-thresholds of filtrations are established for various types of filtrations. Moreover, various…

Motivated by the Maximum Theorem for convex functions (in the setting of linear spaces) and for subadditive functions (in the setting of Abelian semigroups), we establish a Maximum Theorem for the class of generalized convex functions,…

We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…

We show that if $f$ is a nonzero, noninvertible function on a smooth complex variety $X$ and $J_f$ is the Jacobian ideal of $f$, then ${\rm lct}(f,J_f^2)>1$ if and only if the hypersurface defined by $f$ has rational singularities.…

The ring of periodic distributions on ${\mathbb{R}}^{\tt d}$ with usual addition and with convolution is considered. Via Fourier series expansions, this ring is isomorphic to the ring ${\mathcal{S}}'({\mathbb{Z}}^{\tt d})$ of all maps…