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This paper is devoted to the study of some connections between coadjoint orbits in infinite dimensional Lie algebras, isospectral deformations and linearization of dynamical systems. We explain how results from deformation theory,…
We establish an operator algebra generalization of Watrous' theorem \cite{watrous2009} on mixing unital quantum channels (completely positive trace-preserving maps) with the completely depolarizing channel, wherein the more general objects…
This paper presents a general study of one-dimensional differentiability for functionals defined on convex domains that are not necessarily open. The local approximation is carried out using affine functionals, as opposed to linear…
The outlines of a "Galois theory" for bimeromorphic geometry is here developed, via the study of model-theoretic definable binding groups in the theory CCM of compact complex spaces. As an application, a structure theorem about principal…
The main result of the paper is an extension of the Dirichlet problem from (closures of) bounded open domains U to arbitrary compact subsets X of the complex plane, i.e. the closure of the corresponding space of functions which are harmonic…
We construct uncountably generated algebras inside the following sets of special functions: Sierpi\'nski-Zygmund functions, perfectly everywhere surjective functions and nowhere continuous Darboux functions. All conclusions obtained in this…
Curved algebras are a generalization of differential graded algebras which have found numerous applications recently. The goal of this foundational article is to introduce the notion of a curved operad, and to develop the operadic calculus…
Colombeau's generalized functions are used to adapt the distributional approach to singular hypersurfaces in general relativity with signature change. Equations governing the dynamics of singular hypersurface is obtained and it is shown…
We give a quick survey of the various fixed point theorems in computability theory, partial combinatory algebra, and the theory of numberings, as well as generalizations based on those. We also point out several open problems connected to…
For a large class of separable Banach spaces, we prove the real analytic Dolbeault Isomorphism Theorem for open subsets.
This is the second in a series of papers laying the foundations for a differential graded approach to derived differential geometry (and other geometries in characteristic zero). In this paper, we extend the classical notion of a dg-algebra…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
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…
The underlying algebra for a noncommutative geometry is taken to be a matrix algebra, and the set of derivatives the adjoint of a subset of traceless matrices. This is sufficient to calculate the dual 1-forms, and show that the space of…
We extend Yves Andr\'e's theory of solution algebras in differential Galois theory to a general Tannakian context. As applications, we establish analogues of his correspondence between solution fields and observable subgroups of the Galois…
An integro-differential ring is a differential ring that is closed under an integration operation satisfying the fundamental theorem of calculus. Via the Newton--Leibniz formula, a generalized evaluation is defined in terms of integration…
This paper studies first the differential inequalities that make it possible to build a global theory of pseudo-holomorphic functions in the case of one or several complex variables. In the case of one complex dimension, we prove that the…
The theme of this paper is to `solve' an absolutely irreducible differential module explicitly in terms of modules of lower dimension and finite extensions of the differential field $K$. Representations of semi-simple Lie algebras and…
In this paper we study the concept of algebraic core for convex sets in general vector spaces without any topological structure and then present its applications to problems of convex analysis and optimization. Deriving the equivalence…
We propose the use of algebras of generalized functions for the analysis of certain highly singular problems in the calculus of variations. After a general study of extremal problems on open subsets of Euclidean space in this setting we…