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Consider $d$ disjoint closed subintervals of the unit interval and consider an orientation preserving expanding map which maps each of these subintervals to the whole unit interval. The set of points where all iterates of this expanding map…
The Strang-Fix conditions are necessary and sufficient to reproduce spaces of algebraic polynomials up to some degree by integer shifts of compactly supported functions. W. Dahmen and Ch. Micchelli (Linear Algebra Appl. 52/3:217-234, 1983)…
In this paper, we propose necessary and sufficient conditions for a scalar function to be nonincreasing along solutions to general differential inclusions with state constraints. The problem of determining if a function is nonincreasing…
We prove that every nonnegative continuous real-valued function on a given compact metric space is the uniform limit of some increasing sequence of nonnegative simple functions being linear combinations of indicators of open sets; here the…
We consider an infinite spatial inhomogeneous random graph model with an integrable connection kernel that interpolates nicely between existing spatial random graph models. Key examples are versions of the weight-dependent random connection…
In this review article, we discuss the distinction and possible equivalence between scale invariance and conformal invariance in relativistic quantum field theories. Under some technical assumptions, we can prove that scale invariant…
In this paper we are interested in functionals defined on completely distributive lattices and which are invariant under mappings preserving {arbitrary} joins and meets. We prove that the class of nondecreasing invariant functionals…
A shift-invariant space is a space of functions that is invariant under integer translations. Such spaces are often used as models for spaces of signals and images in mathematical and engineering applications. This paper characterizes those…
We show that any affine invariant function on the set of positive definite matrices must factor through the determinant function, as long as the restriction of the function to scalar matrices is surjective. A motivation from robust…
We describe a procedure for determining the generalised scaling functions $f_n(g)$ at all the values of the coupling constant. These functions describe the high spin contribution to the anomalous dimension of large twist operators (in the…
This paper presents a noncommutative theory of symmetric functions, based on the notion of quasi-determinant. We begin with a formal theory, corresponding to the case of symmetric functions in an infinite number of independent variables.…
This paper presents necessary, sufficient, and equivalent conditions for the spherical convexity of non-homogeneous quadratic functions. In addition to motivating this study and identifying useful criteria for determining whether such…
We study the computation of local approximations of invariant manifolds of parabolic fixed points and parabolic periodic orbits of periodic vector fields. If the dimension of these manifolds is two or greater, in general, it is not possible…
In the realm of topological automorphisms of totally disconnected locally compact groups, the scale function introduced by Willis in \cite{Willis} is compared with the topological entropy. We prove that the logarithm of the scale function…
In this paper we consider the question of smoothness of slowly varying functions satisfying the modern definition that, in the last two decades, gained prevalence in the applications concerning function spaces and interpolation. We show,…
In this article we study invariance properties of shift-invariant spaces in higher dimensions. We state and prove several necessary and sufficient conditions for a shift-invariant space to be invariant under a given closed subgroup of…
We examine the question of scale versus conformal invariance on maximally symmetric curved backgrounds and study general 2-derivative conformally invariant free theories of vectors and tensors. For spacetime dimension $D>4$, these conformal…
We consider scale-invariant interactions of 6D N=1 hypermultiplets with the gauge multiplet. If the canonical dimension of the matter scalar field is assumed to be 1, scale-invariant lagrangians involve higher derivatives in the action.…
In this paper we give some conditions for a class of functions related to Bessel functions to be positive definite or strictly positive definite . We present some properties and relationships involving logarithmically completely monotonic…
We consider the breakdown of conformal and scale invariance in random systems with strongly random critical points. Extending previous results on one-dimensional systems, we provide an example of a three-dimensional system which has a…