Related papers: Local regularity in non-linear generalized functio…

In the context of the complex-analytic structure within the unit disk centered at the origin of the complex plane, that was presented in a previous paper, we show that singular Schwartz distributions can be represented within that same…

Newtonian spaces generalize first-order Sobolev spaces to abstract metric measure spaces. In this paper, we study regularity of Newtonian functions based on quasi-Banach function lattices. Their (weak) quasi-continuity is established,…

In this paper we study some local and global regularity properties of Fourier series obtained as fractional integrals of modular forms. In particular we characterize the differentiability at rational points, determine their H\"older…

We introduce a novel projection depth for data lying in a general Hilbert space, called the regularized projection depth, with a focus on functional data. By regularizing projection directions, the proposed depth does not suffer from the…

We study the apparent tension between locality and unitarity for symmetries in quantum field theory. This emerges in the context of categorical symmetries where symmetry operators are generically non-invertible. We argue that locality…

In this article, we review and discuss different aspects of stability and genericity of some properties of space-times which occur in various contexts in the General Theory of Relativity. We also give argument supporting the conclusion that…

Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…

A generalization of a distribution increases the flexibility particularly in studying of a phenomenon and its properties. Many generalizations of continuous univariate distributions are available in literature. In this study, an…

We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the basic properties of finite algebras in these varieties such…

We study the regularity of solutions of functional equations of a generalized mean value type. In this paper we give sufficient conditions for the regularity by using hypoellipticity which is a concept of the theory of partial differential…

We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations…

Generalizations of Ostrowski type inequality for functions of Lipschitzian type are established. Applications in numerical integration and cumulative distribution functions are also given.

We study the local Lipschitz one subsets of a finite dimensional space, that is, sets for which there exists a continuous function whose local Lipschitz derivative is the characteristic function of said set. We give a characterization of a…

In this article, we investigate nonlinear metric subregularity properties of set-valued mappings between general metric or Banach spaces. We demonstrate that these properties can be treated in the framework of the theory of (linear) error…

Symmetry groups allow to transform solutions of differential equations continuously into other solutions. This property can be used for the observability analysis of infinite-dimensional systems with input and output. In this contribution,…

We consider a class of functions defined on metric spaces which generalizes the concept of piecewise Lipschitz continuous functions on an interval or on polyhedral structures. The study of such functions requires the investigation of their…

We introduce the notion of functionally compact sets into the theory of nonlinear generalized functions in the sense of Colombeau. The motivation behind our construction is to transfer, as far as possible, properties enjoyed by standard…

We introduce a new category called Quasi-Nash, unifying Nash manifolds and algebraic varieties. We define Schwartz functions, tempered functions and tempered distributions in this category. We show that properties that hold on affine…

The regularity of refinable functions has been studied extensively in the past. A classical result by Daubechies and Lagarias states that a compactly supported refinable function in $\R$ of finite mask with integer dilation and translations…

Symmetric functions, which take as input an unordered, fixed-size set, are known to be universally representable by neural networks that enforce permutation invariance. These architectures only give guarantees for fixed input sizes, yet in…