Related papers: Sign uncertainty and de Branges spaces
Reliable uncertainty quantification is essential for the use of machine learning in physics, where scientific discoveries depend on validated probabilistic statements. We provide a structured overview of uncertainty quantification in ML for…
Uncertainty principles present an important theoretical tool in signal processing, as they provide limits on the time-frequency concentration of a signal. In many real-world applications the signal domain has a complicated irregular…
The counting function on binary values is extended to the signed case in order to count the number of transitions between contiguous locations. A generalized subdifferential for the sign change counting function is given where classical…
The sign uncertainty principle of Bourgain, Clozel & Kahane asserts that if a function $f:\mathbb{R}^d\to \mathbb{R}$ and its Fourier transform $\widehat{f}$ are nonpositive at the origin and not identically zero, then they cannot both be…
We extend some results of M.G. Krein to the class of entire functions which can be represented as ratios of discrete Cauchy transforms in the plane. As an application we obtain new versions of de Branges' Ordering Theorem for nearly…
A theory of measurement uncertainty is presented, which, since it is based exclusively on the Bayesian approach and on the subjective concept of conditional probability, is applicable in the most general cases. The recent International…
In this paper, uncertainty relations for MIMO ambiguity functions are given. Norm inequalities on the MIMO ambiguity functions in terms of signals of concern are studied. A signal dependent lower bound on the support of MIMO ambiguity…
Let $G$ be a locally compact abelian group, and let $\widehat{G}$ denote its dual group, equipped with a Haar measure. A variant of the uncertainty principle states that for any $S \subset G$ and $\Sigma \subset \widehat{G}$, there exists a…
Sampling theory in spaces other than the space of band-limited functions has recently received considerable attention. This is in part because the band-limitedness assumption is not very realistic in many applications. In addition,…
We utilize the theory of de Branges spaces to show when certain Schr\"odinger operators with strongly singular potentials are uniquely determined by their associated spectral measure. The results are applied to obtain an inverse uniqueness…
We establish bounds for the covariance of a large class of functions of infinite variance stable random variables, including unbounded functions such as the power function and the logarithm. These bounds involve measures of dependence…
Uncertainty principles for concentration of signals into truncated subspaces are considered. The ``classic'' uncertainty principle is explored as a special case of a more general operator framework. The time-bandwidth concentration problem…
This paper is devoted to the study of the parameter's set where the Green's function related to a general linear $n^{\rm th}$-order operator, depending on a real parameter, $T_n[M]$, coupled with many different two point boundary value…
It is known that there exist functions in certain de Branges--Rovnyak spaces whose Taylor series diverge in norm, even though polynomials are dense in the space. This is often proved by showing that the sequence of Taylor partial sums is…
An inequality refining the lower bound for a periodic (Breitenberger) uncertainty constant is proved for a wide class of functions. A connection of uncertainty constants for periodic and non-periodic functions is extended to this class. A…
In this work we consider de Branges spaces where the multiplication operator by the independent variable is not densely defined. First, we study the canonical selfadjoint extensions of the multiplication operator as a family of rank-one…
Rule based classifiers that use the presence and absence of key sub-strings to make classification decisions have a natural mechanism for quantifying the uncertainty of their precision. For a binary classifier, the key insight is to treat…
This paper aims to study the boundedness and compactness of composition operators from model spaces to the Hardy Hilbert spaces in the upper half-plane. Consequently, we investigate the boundedness and compactness of composition operators…
We study the set of curvature functions which a given compact manifold with boundary can possess. First, we prove that the sign demanded by the Gauss-Bonnet Theorem is a necessary and sufficient condition for a given function to be the…
Under certain conditions, we obtain sharp bounds on some functionals defined in the coefficient space of starlike functions. It has been found that the functionals are closely associated with certain coefficient problems, which are of…