Related papers: Determinacy for measures
We prove several results related to the theorem of Logvinenko and Sereda on determining sets for functions with Fourier transforms supported in an interval. We obtain a polynomial instead of exponential bound in this theorem, and we extend…
The moment problem in probability theory asks for criteria for when there exists a unique measure with a given tuple of moments. We study a variant of this problem for random objects in a category, where a moment is given by the average…
Complex moment sequences are exactly those which admit positive definite extensions on the integer lattice points of the upper diagonal half-plane. Here we prove that the aforesaid extension is unique provided the complex moment sequence is…
In the field of orthogonal polynomials theory, the classical Markov theorem shows that for determinate moment problems the spectral measure is under control of the polynomials asymptotics. The situation is completely different for…
We investigate moment sequences of probability measures on $E\subset\mathbb{R}$ under constraints of certain moments being fixed. This corresponds to studying sections of $n$-th moment spaces, i.e. the spaces of moment sequences of order…
We study here a sequence of secondary measures, so called because the set of secondary polynomials on a given term become orthogonal for the next measure. The main result is a formula making explicit the density of any term of the sequence,…
Deriving the time evolution of a distribution of probability (or a probability density matrix) is a problem encountered frequently in a variety of situations: for physical time, it could be a kinetic reaction study, while identifying time…
Let $\mu$ be a positive measure on the real line with locally finite support $\Lambda$ and integer masses such that its Fourier transform in the sense of distributions is a purely point measure. An explicit form is found for an entire…
We prove sharp estimates on the time-average behavior of the squared absolute value of the Fourier transform of some absolutely continuous measures that may have power-law singularities, in the sense that their Radon-Nikodym derivatives…
Spectral measures of Wigner matrices are investigated. The Wigner semicircle law for spectral measures is proved. Regard this as the law of large number, the central limit theorem for moments spectral measure is also derived. The proof is…
We establish an exponential error term for the renewal theorem in the context of products of random matrices, which is surprising compared with classical abelian cases. A key tool is the Fourier decay of the Furstenberg measures on the…
Necessary and sufficient conditions for a measure to be an extreme point of the set of measures (on an abstract measurable space) with prescribed generalized moments are given, as well as an application to extremal problems over such moment…
In our paper we extend some results of the theory of Fourier quasicrystals on the real line to a horizontal strip of finite width. For measures in a strip we use a natural generalization of the usual Fourier transform for measures on the…
We present a family of explicit formulae for evaluating absolute moments of probability measures on $\mathbb{R}^d$ in terms of Fourier transforms. As to the space of probability measures possessing finite absolute moments of an arbitrary…
The problem of characterising the accuracy of, and disturbance caused by a joint measurement of position and momentum is investigated. In a previous paper the problem was discussed in the context of the unbiased measurements considered by…
The problem of replacing an integral norm with respect to a given probability measure by the corresponding integral norm with respect to a discrete measure is discussed in the paper. The above problem is studied for elements of finite…
Work on generalizations of the Cohen-Lenstra and Cohen-Martinet heuristics has drawn attention to probability measures on the space of isomorphism classes of profinite groups. As is common in probability theory, it would be desirable to…
This paper considers convolution equations that arise from problems such as measurement error and non-parametric regression with errors in variables with independence conditions. The equations are examined in spaces of generalized functions…
We establish various forms of the following certainty principle: a set $S \subset \mathbb{R}^{n}$ contains a given finite linear pattern, provided that $S$ is a support of the Fourier transform of a sufficiently singular probability measure…
The multivariate moment problem is investigated in the general context of the polynomial algebra $\mathbb{R}[x_i \mid i \in \Omega]$ in an arbitrary number of variables $x_i$, $i\in \Omega$. The results obtained are sharpest when the index…