Related papers: On subfiniteness of graded linear series
We develope a local theory for frames on finite dimensional Hilbert spaces. In particular, a bounded frame on a finite dimensional Hilbert space contains a subset which is a good Riesz basis for a percentage (arbitrarily close to one) of…
The aim of this paper is to give some properties of Hilbert genus fields and construct the Hilbert genus fields of the fields $L_{m,d}:=\mathbb{Q}(\zeta_{2^m},\sqrt{d})$, where $m\geq 3$ is a positive integer and $d$ is a square-free…
We deal with the existing problem of filtered multiplicative bases of finite-dimensional associative algebras. For an associative algebra A over a field, we investigate when the property of having a filtered multiplicative basis is…
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…
Let $M$ be a von Neumann algebra with a faithful normal finite trace $t$, and $H^\infty$ be a finite, maximal, subdiagonal of $M$. Fundamental theorems on conjugate functions for weak* Dirichlet algebras are shown to be a bounded linear map…
The starting point of this work is that the class of evolution algebras over a fixed field is closed under tensor product. This arises questions about the inheritance of properties from the tensor product to the factors and conversely. For…
Given a Hilbertian field $k$ and a finite set $\mathcal{S}$ of Krull valuations of $k$, we show that every finite split embedding problem $G \rightarrow {\rm{Gal}}(L/k)$ over $k$ with abelian kernel has a solu\-tion ${\rm{Gal}}(F/k)…
We demonstrate that certain classes of Schl\" omilch-like infinite series and series that include generalized hypergeometric functions can be calculated in closed form starting from a simple quantum model of a particle trapped inside an…
The category $\bcalNT$ was defined in \cite{Lobos2}, it is a category whose objects are commutative nil graded algebras over a field, defined by presentation encoded by triangular matrices. A natural problem related to this category is to…
In this article, the reproducing kernel Hilbert space [0, 1] is employed for solving a class of third-order periodic boundary value problem by using fitted reproducing kernel algorithm. The reproducing kernel function is built to get fast…
We prove that Hilbert's Tenth Problem for a ring of integers in a number field K has a negative answer if K satisfies two arithmetical conditions (existence of a so-called division-ample set of integers and of an elliptic curve of rank one…
We prove that every total sequence in a Hilbert space satisfies the lower frame inequality after scaling. This solves A. Kulikov's "exercise" at mathoverflow.
We prove that the weak Hilbert property ascends along a morphism of varieties over an arbitrary field of characteristic zero, under suitable assumptions.
Fractionally-quadratic transformations which reduce any two-dimensional quadratic system to the special Lienard equation are introduced. Existence criteria of cycles are obtained.
This is a study of terminating and ill-defined Gauss hypergeometric functions. Corresponding hypergeometric equations have a degenerate set of of 24 Kummer's solutions. We describe those solutions and relations between them.
The one-sided and full Hilbert transforms are evaluated exactly by means of the method of finite-part integration [E.A. Galapon, \textit{Proc. Roy. Soc. A} \textbf{473}, 20160567 (2017)]. In general, the result consists of two terms -- the…
We consider associative algebras with involution graded by a finite abelian group G over a field of characteristic zero. Suppose that the involution is compatible with the grading. We represent conditions permitting PI-representability of…
Many classical results in algebraic geometry arise from investigating some extremal behaviors that appear among projective varieties not lying on any hypersurface of fixed degree. We study two numerical invariants attached to such…
This expository essay discusses a finite dimensional approach to dilation theory. How much of dilation theory can be worked out within the realm of linear algebra? It turns out that some interesting and simple results can be obtained. These…
Given any finite quiver, we consider a complete flag of vector spaces over each vertex. Consider the unipotent invariant subalgebra of the coordinate ring of the filtered quiver representation subspace. We prove that the dimension of the…