Related papers: A constructive approach to triangular trigonometri…
Given a triangulated category over a field $K$ and a field extension $L/K$, we investigate how one can construct a triangulated category over $L$. Our approach produces the derived category of the base change scheme $X_L$ if the category…
Let $P_N(R)$ be the space of all real polynomials in $N$ variables with the usual inner product $<, >$ on it, given by integrating over the unit sphere. We start by deriving an explicit combinatorial formula for the bilinear form…
We consider the vector space of globally differentiable piecewise polynomial functions defined on a three-dimensional polyhedral domain partitioned into tetrahedra. We prove new lower and upper bounds on the dimension of this space by…
Maximal $(k+1)$-crossing-free graphs on a planar point set in convex position, that is, $k$-triangulations, have received attention in recent literature, with motivation coming from several interpretations of them. We introduce a new way of…
We propose a patchwise local Fourier extension method for approximating smooth functions on general two dimensional domains with curved boundaries. The domain is embedded into a Cartesian background grid and decomposed into rectangular…
We establish the first extension results for divergence-free (or solenoidal) elements of $\mathrm{L}^{1}$-based function spaces. Here, the key point is to preserve the solenoidality constraint while simultaneously keeping the underlying…
We study three finite-dimensional quotient vector spaces constructed from the linear span of the set of characteristic functions of permutohedral cones by imposing two kinds of constraints: (1) neglect characteristic functions of higher…
Two pertinent questions for any support theory of a monoidal triangulated category are whether it is functorial and if the tensor product property holds. To this end, we consider the complete prime spectrum of an essentially small monoidal…
In this paper we consider a construction in an arbitrary triangulated category T which resembles the notion of a Moore spectrum in algebraic topology. Namely, given a compact object C of T satisfying some finite tilting assumptions, we…
We present some results on equivariant KK-theory in the context of tensor triangular geometry. More specifically, for G a finite group, we show that the spectrum of the tensor triangulated subcategory of KK^G generated by the tensor unit…
An effective means to approximate an analytic, nonperiodic function on a bounded interval is by using a Fourier series on a larger domain. When constructed appropriately, this so-called Fourier extension is known to converge geometrically…
In this paper, a method for constructing a near optimal normal basis for algebraic extensions of a finite field is described. In each extension, except for the squares of basis elements, the product of two distinct normal basis elements can…
In this paper, we introduce a method known as polynomial frame approximation for approximating smooth, multivariate functions defined on irregular domains in $d$ dimensions, where $d$ can be arbitrary. This method is simple, and relies only…
We present a triangulation--independent area--ordering prescription which naturally generalizes the well known path ordering one. For such a prescription it is natural that the two--form ``connection'' should carry three ``color'' indices…
We study sets $V$ in the tridisc that are relatively polynomially convex and have the polynomial extension property. If $V$ is one-dimensional, and is either algebraic, or has polynomially convex projections, we show that it is a retract.…
The classical Haar construction of Brownian motion uses a binary tree of triangular wedge-shaped functions. This basis has compactness properties which make it especially suited for certain classes of numerical algorithms. We present a…
This paper puts forward a new generalized polynomial dimensional decomposition (PDD), referred to as GPDD, comprising hierarchically ordered measure-consistent multivariate orthogonal polynomials in dependent random variables. Unlike the…
The main contribution of this note is to establish a framework to extend results of tensor functions over specific field to general field. As a consequence of this framework, we extend the existing work to more general settings: \emph{(1)}…
We introduce a generalization $G^{(\alpha)}(X)$ of the truncated logarithm $\mathcal{L}_1(X) = \sum_{k=1}^{p-1}X^k/k$ in characteristic $p$, which depends on a parameter $\alpha$. The main motivation of this study is $G^{(\alpha)}(X)$ being…
Systematic expansion schemes in functional approaches require the inclusion of higher order vertices. These vertices are expanded in independent tensor bases with a rapidly increasing number of basis elements. Amongst the related tasks are…