相关论文: The geometry of Hilbert functions

We consider the gradient flow of hypersurfaces immersed in the Euclidean space associated to geometric energy functionals. We show that for particular functionals depending by higher covariant derivatives of the curvature, singularities in…

We obtain a general concept of triplet of Hilbert spaces with closed (unbounded) embeddings instead of continuous (bounded) ones. The construction starts with a positive selfadjoint operator $H$, that is called the Hamiltonian of the…

Consider the projection of a smooth irreducible surface in $\mathbb{P}^3$ from a point. The uniform position principle implies that the monodromy group of such a projection from a general point in $\mathbb{P}^3$ is the whole symmetric…

We study the typical behavior of bounded linear operators on infinite dimensional complex separable Hilbert spaces in the norm, strong-star, strong, weak polynomial and weak topologies. In particular, we investigate typical spectral…

We show that dynamical and counting results characteristic of negatively-curved Riemannian geometry, or more generally CAT($-1$) or rank-one CAT($0$) spaces, also hold for rank-one properly convex projective structures, equipped with their…

We isolate a geometric mechanism that complements the dynamical suppression of macroscopic interference: In a high-dimensional Hilbert space, almost all state vectors are nearly orthogonal, accommodating an exponentially large reservoir of…

For different cohomology theories (including the Hochschild homology, Hodge cohomology, Chow groups, and Grothendieck groups of coherent sheaves), we identify the cohomology of moduli space of rank 1 perverse coherent sheaves on the blow-up…

We compute the Hochschild cohomology of Hilbert schemes of points on surfaces and observe that it is, in general, not determined solely by the Hochschild cohomology of the surface, but by its "Hochschild-Serre cohomology": the bigraded…

In this article, we prove an extension of the mean value theorem and a comparison theorem for subharmonic functions. These theorems are used to answer the question whether we can conclude that two subharmonic functions which agree almost…

The purpose of these notes is to give a short survey of an interesting connection between partition functions of supersymmetric gauge theories and hypergeometric functions and to present the recent progress in this direction.

In this article, we present some new inequalities for numerical radius of Hilbert space operators via convex functions. Our results generalize and improve earlier results by El-Haddad and Kittaneh. Among several results, we show that if…

We analyse the geometry of Hilbert schemes of points on abelian surfaces and Beauville's generalized Kummer varieties in positive characteristics. The main result is that, in characteristic two, the addition map from the Hilbert scheme of…

We propose a notion of functor of points for noncommutative spaces, valued in categories of bimodules, and endowed with an action functional determined by a notion of hermitian structures and height functions, modeled on an interpretation…

This paper systematically studies Hilbert boundary value problems for hyper monogenic functions on the hyperplane for the solutions being of any integer orders at the infinity, where the negative order cases are new even when restricted to…

This paper gives a self-contained introduction to the Hilbert projective metric $\mathcal{H}$ and its fundamental properties, with a particular focus on the space of probability measures. We start by defining the Hilbert pseudo-metric on…

We study the generalization of $m$-isometries and $m$-contractions (for positive integers $m$) to what we call $a$-isometries and $a$-contractions for positive real numbers $a$. We show that any Hilbert space operator, satisfying an…

Given the growing quantity of proposals and works of basic hypergeometric functions in the scope of $q$-calculus, it is important to introduce a systematic classification of $q$-calculus. Our aim in this article is to investigate certain…

In this paper, structural properties of lower semi-frames in separable Hilbert spaces are explored with a focus on transformations under linear operators (may be unbounded). Also, the direct sum of lower semi-frames, providing necessary and…

Suppose $H$ is a finite dimensional reproducing kernel Hilbert space of functions on $X.$ If $H$ has the complete Pick property then there is an isometric map, $\Phi,$ from $X,$ with the metric induced by $H,$ into complex hyperbolic space,…

I give a theory of Moebius-flat hypersurfaces in n-dimensional projective space, analogous to that in conformal geometry. This unifies the classes of hypersurfaces with flat induced conformal structure (n > 3) and a classically studied…