相关论文: Extensor in Geometric Algebras

Practically and intrinsically, inclusions of operator algebras are of fundamental interest. The subject of this paper is intermediate operator algebras of inclusions. There are two previously known theorems which naturally and completely…

We develop a rigorous framework for extending neural operators to handle out-of-distribution input functions. We leverage kernel approximation techniques and provide theory for characterizing the input-output function spaces in terms of…

Given Hilbert space operators $P,T\in B(\H), P\geq 0$ invertible, $T$ is $(m,P)-$ expansive (resp., $(m,P)-$ isometric) for some positive integer $m$ if…

Parametric Gr\"obner bases have been studied for more than 15 years and are now a further developed subject. Here we propose a general study of parametric standard bases, that is with local orders. We mainly focus on the commutative case…

Indicial operators are model operators associated to an elliptic differential operator near a corner singularity on a stratified manifold. These model operators are defined on generalized tangent cone configurations and exhibit a natural…

The notion of invariant operators, or Fourier multipliers, is discussed for densely defined operators on Hilbert spaces, with respect to a fixed partition of the space into a direct sum of finite dimensional subspaces. As a consequence,…

In this paper we study the Taylor series of an operator-valued function related to the differential of the exponential map. For a smooth manifold $\mathcal{M}$ with a torsion-free affine connection the operator $\mathcal{E}_p(v)$ acting on…

The goal of this text is to understand and prove a formula stated by Salmon, which gives the first terms of some Taylor expansion of the discriminant of a plane algebraic curve. Salmon uses his formula to derive various enumerative…

This paper introduces the concept of grand net spaces, a new framework that provides a unified setting for studying various function spaces. Building on the seminal works of [8] and [15], we define grand net spaces and establish their key…

Here we continue to list the differential operators invariant with respect to the 15 exceptional simple Lie superalgebras of polynomial vector fields. A part of the list (for operators acting on tensors with finite dimensional fibers) was…

Extending the construction of the (intrinsically defined) full algebra of scalar valued Colombeau functions on a smooth manifold M (Grosser et al., Adv. Math. 166 (2002), 179-206) we present a suitable basic space for eventually obtaining…

We consider differential operators between sections of arbitrary powers of the determinant line bundle over a contact manifold. We extend the standard notions of the Heisenberg calculus: noncommutative symbolic calculus, the principal…

In this paper we study the boundedness of extension operators associated with spheres in vector spaces over finite fields.In even dimensions, we estimate the number of incidences between spheres and points in the translated set from a…

The aim of the present paper is to define compact operators on asymmetric normed spaces and to study some of their properties. The dual of a bounded linear operator is defined and a Schauder type theorem is proved within this framework. The…

We define tensors, corresponding to cubic polynomials, which have the same exponent $\omega$ as the matrix multiplication tensor. In particular, we study the symmetrized matrix multiplication tensor $sM_n$ defined on an $n\times n$ matrix…

We consider the recursion operators with nonlocal terms of special form for evolution systems in (1+1) dimensions, and extend them to well-defined operators on the space of nonlocal symmetries associated with the so-called universal Abelian…

This paper deals with well-known higher-order generalizations of Hankel operators. We show that higher-order Hankel operators can be written explicitly as linear differential operators, and give the exact form of these differential…

We consider the Schr\"odinger operator on a combinatorial graph consisting of a finite graph and a finite number of discrete half-lines, all jointed together, and compute an asymptotic expansion of its resolvent around the threshold $0$.…

In this paper we give a survey of elliptic theory for operators associated with diffeomorphisms of smooth manifolds. Such operators appear naturally in analysis, geometry and mathematical physics. We survey classical results as well as…

We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…