Related papers: Linear spectral transformations of Carath\'eodory …
This paper studies the nature of fractional linear transformations in a general relativity context as well as in a quantum theoretical framework. Two features are found to deserve special attention: the first is the possibility of…
The in-medium modifications of hadron properties such as masses and decay widths have been a major focus of the scientific work of Gerry Brown and the insights gained by him and his collaborators made them major drivers of this field for…
In this article, we determine the multivariate multifractal Legendre spectra of shifted L{\'e}vy functions. This allows us to explore how the validity of the multivariate multifractal formalism depends on the shift parameter. This article…
Spectral measures arise in numerous applications such as quantum mechanics, signal processing, resonances, and fluid stability. Similarly, spectral decompositions (pure point, absolutely continuous and singular continuous) often…
We give a class of domains for which Fridman invariant and injectivity radius function coincide with respect to Carath\'eodory metric. We give explicit expressions of the squeezing functions for these domains and investigate some of their…
We study the spectral statistics for extended yet finite quasi 1-d systems which undergo a transition from periodicity to disorder. In particular we compute the spectral two-point form factor, and the resulting expression depends on the…
The Carath\'eodory theorem on the construction of a measure is generalized by replacing the outer measure with an approximation of it and generalizing the Carath\'eodory measurability. The new theorem is applied to obtain dynamically…
We show that under quite general conditions, various multifractal spectra may be obtained as Legendre transforms of functions $T\colon \RR\to \RR$ arising in the thermodynamic formalism. We impose minimal requirements on the maps we…
In this paper, we introduce and study the Fourier transform of functions which are integrable with respect to a vector measure on a compact group (not necessarily abelian). We also study the Fourier transform of vector measures. We also…
This paper determines how to define a discretely implemented Fourier transform when analysing an observed spatial point process. To develop this transform we answer four questions; first what is the natural definition of a Fourier…
The relationship between smooth measures and positive continuous additive functionals is well known, and this correspondence is called the Revuz correspondence. We investigate the relationships between several types of convergence of smooth…
The interplay of nuclear and electronic dynamics characterizes the multi-dimensional electronic spectra of various molecular and solid-state systems. Theoretically, the observable effect of such interplay can be accounted for by response…
By designating vertices with variables, a simple undirected graph can be augmented to have an associated representing rational function in two variables taking the complex bi-upper halfplane to itself. We give relations between representing…
Theorems and explicit examples are used to show how transformations between self-similar sets (general sense) may be continuous almost everywhere with respect to stationary measures on the sets and may be used to carry well known flows and…
We derive a general relation between correlators of density of states fluctuations and density response functions. It applies equally to quantum chaotic systems of pure symmetry (unitary, orthogonal, and symplectic) as well as to the…
Functionals (i.e. functions of functions) are widely used in quantum field theory and solid-state physics. In this paper, functionals are given a rigorous mathematical framework and their main properties are described. The choice of the…
The new results concerning the continuity of holomorphically contractible systems treated as set functions with respect to non-monotonic sequences of sets are given. In particular, continuity properties of Kobayashi and Carath\'eodory…
A scalar-response functional model describes the association between a scalar response and a set of functional covariates. An important problem in the functional data literature is to test the nullity or linearity of the effect of the…
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
Conformal transformations are obtained by demanding that the form of the metric change by a conformal factor. Nevertheless, this transformation of the metric is not taken into account when a variation of the action is performed. The basic…