Related papers: On the Moment Functionals with Signed Representing…

A characterization of t-normed integrals was obtained in \cite{CLM} for finite compacta and in \cite{Rad} for the general case. Such characterization establishes a correspondence between the space of capacities and homogeneous respect…

All extremal solutions of the truncated $L$-problem of moments in two real variables , with support contained in a given compact set, are described as characteristic functions of semi-algebraic sets given by a single polynomial inequality.…

Let k be an algebraically closed field of characteristic zero. An element F from k(x_1,...,x_n) is called a closed rational function if the subfield k(F) is algebraically closed in the field k(x_1,...,x_n). We prove that a rational function…

In this paper, we show that there is a one-to-one correspondence between operator monotone functions on the nonnegative reals and finite Borel measures on the unit interval. This correspondence appears as an integral representation of…

In an earlier paper, we studied solutions g to convolution equations of the form a_d*g^{*d}+a_{d-1}*g^{*(d-1)}+...+a_1*g+a_0=0, where a_0, ..., a_d are given arithmetic functions associated with Dirichlet series which converge on some right…

In this note we show that if $G$ is a solvable group acting on the line, and if there is $T\in G$ having no fixed points, then there is a Radon measure $\mu$ on the line quasi-invariant under $G$. In fact, our method allows for the same…

Starting with the correspondence between positive definite kernels on the one hand and reproducing kernel Hilbert spaces (RKHSs) on the other, we turn to a detailed analysis of associated measures and Gaussian processes. Point of departure:…

To any algebraic variety X and and closed 2-form \omega on X, we associate the "symplectic action functional" T(\omega) which is a function on the formal loop space LX introduced by the authors in math.AG/0107143. The correspondence \omega…

We present new necessary and sufficient conditions for a function on $\partial\Omega\times S^1$ to be in the range of the attenuated Radon transform of a sufficiently smooth function support in the convex set…

T. M. Bisgaard proved that the $*$-algebra ${\bf C}[z,\overline{z},1/z\overline{z}]$ has the moment property, that is, each positive linear functional on this $*$-algebra is a moment functional. We generalize this result to polynomials in…

This paper is devoted to a Radon-type transform arising in Photoacoustic Tomography that uses integrating line detectors. We consider two situations: when the line detectors are tangent to the boundary of a cylindrical domain and when the…

Signed difference sets have interesting applications in communications and coding theory. A $(v,k,\lambda)$-difference set in a finite group $G$ of order $v$ is a subset $D$ of $G$ with $k$ distinct elements such that the expressions…

We study the endomorphism ring $End(G_A)$ of a subgroup $G_A$ of $\mathbb{Q}^n$ defined by a non-singular $n\times n$-matrix $A$ with integer entries. In the case when the characteristic polynomial of $A$ is irreducible and an extra…

We show that the set of points where the blow-up, in the sense of Preiss, of a signed Radon measure on $\mathbb{R}^n$ is unique and its invariant subspace has dimension $k$ is $k$-rectifiable. As simple applications, we obtain a…

Let $\mathsf{A}=\{a_1,\dots,a_m\}$, $m\in\mathbb{N}$, be measurable functions on a measurable space $(\mathcal{X},\mathfrak{A})$. If $\mu$ is a positive measure on $(\mathcal{X},\mathfrak{A})$ such that $\int a_i d\mu<\infty$ for all $i$,…

In this article generalized attenuated ray transforms (ART) and integral angular moments are investigated. Starting from the Radon transform, the attenuated ray transform and the longitudinal ray transform, we derive the concept of…

The aim of this paper is to prove the existence of solution for a partial differential equation involving a singularity with a general nonnegative, Radon measure $\mu$ as its nonhomogenous term which is given as \begin{eqnarray} -\Delta…

Let $\bbK=\mathbb R, \mathbb C, \mathbb H$ be the field of real, complex or quaternionic numbers and $M_{p, q}(\bbK)$ the vector space of all $p\times q$-matrices. Let $X$ be the matrix unit ball in $M_{n-r, r}(\bbK)$ consisting of…

A classical question in combinatorial number theory asks whether an equation has a solution inside a particular subset of its domain. The Rado's Theorem gives a set of necessary and sufficient conditions for a systems of linear equations to…

A $(v,k,\lambda)$ difference set in a group $G$ of order $v$ is a subset $\{d_1, d_2, \ldots,d_k\}$ of $G$ such that $D=\sum d_i$ in the group ring $\mathbb{Z}[G]$ satisfies $$D D^{-1} = n + \lambda G,$$ where $n=k-\lambda$. If $D=\sum s_i…