Related papers: Ultradifferentiable extension theorems: a survey
Non-Archimedean mathematics (in particular, nonstandard analysis) allows to construct some useful models to study certain phenomena arising in PDE's; for example, it allows to construct generalized solutions of differential equations and…
It was recently shown that arbitrary first-order models canonically extend to models (of the same language) consisting of ultrafilters. The main precursor of this construction was the extension of semigroups to semigroups of ultrafilters, a…
We formulate a multi-valued version of the Tietze-Urysohn extension theorem. Precisely, we prove that any upper semicontinuous multi-valued map with nonempty closed convex values defined on a closed subset (resp. closed perfectly normal…
In this article, we study disjoint universality for certain sequences of operators, that are connected with the differential operator. Actually, the motivation to study such sequences comes from Universal Taylor series, if you change the…
The theory of distributions provides generalized solutions for problems which do not have a classical solution. However, there are problems which do not have solutions, not even in the space of distributions. As model problem you may think…
In the context of internal crossed modules over a fixed base object in a given semi-abelian category, we use the non-abelian tensor product in order to prove that an object is perfect (in an appropriate sense) if and only if it admits a…
We show how to solve explicitly an equation satisfied by a real function belonging to certain general quasianalytic classes. Examples of the classes under consideration are the collection of convergent generalised power series, a class of…
In this paper we study the universal central extension of a Lie--Rinehart algebra and we give a description of it. Then we study the lifting of automorphisms and derivations to central extensions. We also give a definition of a non-abelian…
The Borel problem for Denjoy--Carleman and Braun--Meise--Taylor classes has well-known optimal solutions. The unified treatment of these ultradifferentiable classes by means of one-parameter families of weight sequences allows to compare…
We use nonstandard methods, based on iterated hyperextensions, to develop applications to Ramsey theory of the theory of monads of ultrafilters. This is performed by studying in detail arbitrary tensor products of ultrafilters, as well as…
We derive the analog of the large $N$ Gross-Taylor holomorphic string expansion for the refinement of $q$-deformed $U(N)$ Yang-Mills theory on a compact oriented Riemann surface. The derivation combines Schur-Weyl duality for quantum groups…
In this paper, we obtain two extension theorems for cohomology classes and holomorphic sections defined on analytic subvarieties, which are defined as the supports of the quotient sheaves of multiplier ideal sheaves of…
We study boundary values of harmonic functions in spaces of quasianalytic functionals and spaces of ultradistributions of non-quasianalytic type. As an application, we provide a new approach to H\"ormander's support theorem for…
We prove a general theorem that gives a non trivial relation in the group of derived autoequivalences of a variety (or stack) X, under the assumption that there exists a suitable functor from the derived category of another variety Y…
This expository article is devoted to the local theory of ultradifferentiable classes of functions, with a special emphasis on the quasianalytic case. Although quasianalytic classes are well-known in harmonic analysis since several decades,…
A quantization of field theory based on the DeDonder-Weyl covariant Hamiltonian formulation is discussed. A hypercomplex extension of quantum mechanics, in which the space-time Clifford algebra replaces that of the complex numbers, appears…
We consider some special type extensions of an arbitrary Lie algebra, which we call universal extensions. We show that these extensions are in one-to-one correspondence with finite dimensional associative commutative algebras. We also…
In this paper, we demonstrate that using differential operators one can construct the complete unified web for expansions of amplitudes for a wide range of theories. We first re-derive the expansion of multi-trace Einstein-Yang-Mills…
This thesis expands the available techniques at weak coupling by investigating the linear space of Feynman integrals and the role that (super)symmetry plays in reducing the number of integrals necessary to calculate correlators in the…
We present an axiomatic approach to finite- and infinite-dimensional differential calculus over arbitrary infinite fields (and, more generally, suitable rings). The corresponding basic theory of manifolds and Lie groups is developed.…