Related papers: On kernel theorems for Frechet and DF spaces
In this paper we study finite dimensional algebras, in particular finite semifields, through their correspondence with nonsingular threefold tensors. We introduce a alternative embedding of the tensor product space into a projective space.…
Motivated by applications to duality theorems for $p$-adic pro-\'etale cohomology of rigid analytic spaces, we study the category of Topological Vector Spaces in the setting of condensed mathematics. We prove that it contains, as full…
We introduce Functional Diffusion Processes (FDPs), which generalize score-based diffusion models to infinite-dimensional function spaces. FDPs require a new mathematical framework to describe the forward and backward dynamics, and several…
We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…
Taylor's theorem (and its variants) is widely used in several areas of mathematical analysis, including numerical analysis, functional analysis, and partial differential equations. This article explains how Taylor's theorem in its most…
With a simple generic approach, we develop a classification that encodes and measures the strength of completeness (or compactness) properties in various types of spaces and ordered structures. The approach also allows us to encode notions…
We introduce the Frenet theory of curves in dual space $\d^3$. After defining the curvature and the torsion of a curve, we classify all curves in dual plane with constant curvature. We also establish the fundamental theorem of existence in…
Kernel methods are a highly effective and widely used collection of modern machine learning algorithms. A fundamental limitation of virtually all such methods are computations involving the kernel matrix that naively scale quadratically…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
We give a version of the Montel theorem for Hardy spaces of holomorphic functions on an infinite dimensional space. As a by-product, we provide a Montel-type theorem for the Hardy space of Dirichlet series. This approach also gives an…
Fractional vector calculus is discussed in the spherical coordinate framework. A variation of the Legendre equation and fractional Bessel equation are solved by series expansion and numerically. Finally, we generalize the hypergeometric…
This is the first part in a series of papers in which we introduce and develop a natural, general tensor category theory for suitable module categories for a vertex (operator) algebra. This theory generalizes the tensor category theory for…
This note characterizes multiplicative linear functionals on reproducing kernel Hilbert spaces of functions on the Euclidean unit ball in complex d-dimensional space, in terms of their action on kernel functions. The kernels considered are…
A kernel based method is proposed for the construction of signature (defining) functions of subsets of $\mathbb{R}^d$. The subsets can range from full dimensional manifolds (open subsets) to point clouds (a finite number of points) and…
Topologies on algebraic and equational theories are used to define germ determined, near-point determined, and point determined rings of smooth functions, without requiring them to be finitely generated. It is proved, that any commutative…
Fixed point theorems are one of the many tools used to prove existence and uniqueness of differential equations. When the data involved contains products of distributions, some of these tools may not be useful. Thus rises the necessity to…
An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.
We construct a generalization of the Dolbeault-Grothendieck resolution on a singular complex space. The same construction yields, for each morphism of analytic spaces, a pullback mapping between the respective Dolbeault-Grothendieck…
New index transforms with Weber type kernels, consisting of products of Bessel functions of the first and second kind are investigated. Mapping properties and inversion formulas are established for these transforms in Lebesgue spaces. The…
A recent paper of Church, Ellenberg, and Farb uses topology and representation theory of the symmetric group to prove enumerative results about square-free polynomials and F-stable maximal tori of the general linear group over the algebraic…