Related papers: Sheaves of nonlinear generalized function spaces

We give an overview of the development of algebras of generalized functions in the sense of Colombeau and recent advances concerning diffeomorphism invariant global algebras of generalized functions and tensor fields. We furthermore provide…

We construct a diffeomorphism invariant (Colombeau-type) differential algebra canonically containing the space of distributions in the sense of L. Schwartz. Employing differential calculus in infinite dimensional (convenient) vector spaces,…

We develop the diffeomorphism invariant Colombeau-type algebra of nonlinear generalized functions in a modern and compact way. Using a unifying formalism for the local setting and on manifolds, the construction becomes simpler and more…

We introduce a nonstandard extension of the category of diffeological spaces, and demonstrate its application to the study of generalized functions. Just as diffeological spaces are defined as concrete sheaves on the site of Euclidean open…

We present an extension of J. F. Colombeau's theory of nonlinear generalized functions to spaces of generalized sections of vector bundles. Our construction builds on classical functional analytic notions, which is the key to having a…

This paper lays the foundations for a nonlinear theory of differential geometry that is developed in a subsequent paper which is based on Colombeau algebras of tensor distributions on manifolds. We adopt a new approach and construct a…

We construct generalised diffeomorphisms for E$_9$ exceptional field theory. The transformations, which like in the E$_8$ case contain constrained local transformations, close when acting on fields. This is the first example of a…

We extend the construction of [19] by introducing spaces of generalized tensor fields on smooth manifolds that possess optimal embedding and consistency properties with spaces of tensor distributions in the sense of L. Schwartz. We thereby…

This paper is part of an ongoing program to develop a theory of generalized differential geometry. We consider the space $\mathcal{G}[X,Y]$ of Colombeau generalized functions defined on a manifold $X$ and taking values in a manifold $Y$.…

Algebras of generalized functions offer possibilities beyond the purely distributional approach in modelling singular quantities in non-smooth differential geometry. This article presents an introductory survey of recent developments in…

Co lombeau's construction of generalized functions (in its special variant) is extended to a theory of generalized sections of vector bundles. As particular cases, generalized tensor analysis and exterior algebra are studied. A point value…

We define and characterize spaces of manifold-valued generalized functions and generalized vector bundle homomorphisms in the setting of the full diffeomorphism-invariant vector-valued Colombeau algebra. Furthermore, we establish point…

We use spectral theory to produce embeddings of distributions in the algebras of generalized functions on a closed Riemannian manifold. These embeddings are invariant under isometries and preserve the singularity structure of the…

This paper builds on the theory of generalised functions begun in [1]. The Colombeau theory of generalised scalar fields on manifolds is extended to a nonlinear theory of generalised tensor fields which is diffeomorphism invariant and has…

We extend the theory of fields/distributions developed the paper "A Feigin-Frenkel theorem with n singularities" to a general base scheme. In order to do so we introduce suitable notions of topological sheaves on schemes and study their…

This paper gives a comprehensive analysis of algebras of Colombeau-type generalized functions in the range between the diffeomorphism-invariant quotient algebra $\mathcal{G}^d = \mathcal{E}_M/\mathcal{N}$ introduced in part I and…

We tackle the problem of finding a suitable categorical framework for generalized functions used in mathematical physics for linear and non-linear PDEs. We are looking for a Cartesian closed category which contains both Schwartz…

We study a deformation of infinitesimal diffeomorphisms of a smooth manifold. The deformation is based on a general twist. This leads to a differential geometry on a noncommutative algebra of functions whose product is a star-product. The…

A topological description of various generalized function algebras over corresponding basic locally convex algebras is given. The framework consists of algebras of sequences with appropriate ultra(pseudo)metrics defined by sequences of…

In this paper, we describe a general theory of "spaces with structure sheaves." Specializations of this theory include the classical theory of schemes, the theory of Deligne-Mumford stacks, and their derived generalizations.