Related papers: Poset Embeddings of Hilbert Functions

This paper gives embedding theorems for a very general class of weighted Bergman spaces: the results include a number of classical Carleson embedding theorems as special cases. We also consider little Hankel operators on these Bergman…

In this expositional paper, we discuss commutative algebra -- a study inspired by the properties of integers, rational numbers, and real numbers. In particular, we investigate rings and ideals, and their various properties. After, we…

We study the ring extensions R \subseteq T having the same set of prime ideals provided Nil(R) is a divided prime ideal. Some conditions are given under which no such T exist properly containing R. Using idealization theory, the examples…

We study integration in a class of Hilbert spaces of analytic functions defined on the $\mathbb{R}^s$. The functions are characterized by the property that their Hermite coefficients decay exponentially fast. We use Gauss-Hermite…

Given a polynomial ring $S = \Bbbk[x_1, \dots, x_n]$ over a field $\Bbbk$, and a monomial ideal $M$ of $S$, we say the quotient ring $R = S/M$ is Macaulay-Lex if for every graded ideal of $R$, there exists a lexicographic ideal of $R$ with…

We introduce a natural class of functions, the {\em pseudomultipliers}, associated with a general Hilbert function space, prove an extension theorem which justifies the definition, give numerous examples and establish the nature of the…

We prove an inequality between Hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field, within the framework of embeddings of posets of Hilbert functions. As a main…

We study those operators on a Hilbert space that can be lifted / extended to any twisted Hilbert space. We prove that these form an ideal of operators which contains all the Schatten classes. We characterize those multiplication operators…

Let $S=K[x_1,\ldots,x_n]$ be the polynomial ring over the field $K$, and let $I\subset S$ be a graded ideal. It is shown that for $k \gg0$ the postulation number of $I^k$ is bounded by a linear function of $k$, and it is a linear function…

We consider modules $M$ over Lie algebroids ${\mathfrak g}_A$ which are of finite type over a local noetherian ring $A$. Using ideals $J\subset A$ such that ${\mathfrak g}_A \cdot J\subset J $ and the length $\ell_{{\mathfrak g}_A}(M/JM)<…

Let $(R, m)$ be a $d$-dimensional Cohen-Macaulay local ring. In this note we prove, in a very elementary way, an upper bound of the first normalized Hilbert coefficient of a $m$-primary ideal $I\subset R$ that improves all known upper…

We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic…

A careful study is made of embeddings of posets which have a convex range. We observe that such embeddings share nice properties with the homomorphisms of more restrictive categories; for example, we show that every order embedding between…

We investigate the Hilbert complex of elasticity involving spaces of symmetric tensor fields. For the involved tensor fields and operators we show closed ranges, Friedrichs/Poincare type estimates, Helmholtz type decompositions, regular…

We describe the graded characters and Hilbert functions of certain graded artinian Gorenstein quotients of the polynomial ring which are also representations of the symmetric group. Specifically, we look at those algebras whose socles are…

This paper is a survey on major results on Hilbert functions of multigraded algebras and mixed multiplicities of ideals, including their applications to the computation of Milnor numbers of complex analytic hypersurfaces with isolated…

We classify the Hilbert functions of bigraded algebras in $k[x_1, x_2, y_1, y_2]$ introducing a numerical function called Ferrers function.

We describe explicitly how certain standard opens of the Hilbert scheme of points are embedded into Grassmannians. The standard opens of the Hilbert scheme that we consider are given as the intersection of a corresponding basic open affine…

We develop novel learning rates for conditional mean embeddings by applying the theory of interpolation for reproducing kernel Hilbert spaces (RKHS). We derive explicit, adaptive convergence rates for the sample estimator under the…

We study irreducible specializations, in particular when group-preserving specializations may not exist. We obtain a criterion in terms of embedding problems. We include several applications to analogs of Schinzel's hypothesis H and to the…