Related papers: A Gaussian Radon Transform for Banach Spaces

The study of Gaussian measures on Banach spaces is of active interest both in pure and applied mathematics. In particular, the spectral theorem for self-adjoint compact operators on Hilbert spaces provides a canonical decomposition of…

We consider a class of Gaussian random holomorphic functions, whose expected zero set is uniformly distributed over $\C^n $. This class is unique (up to multiplication by a non zero holomorphic function), and is closely related to a…

The Radon transform and its dual are central objects in geometric analysis on Riemannian symmetric spaces of the noncompact type. In this article we study algebraic versions of those transforms on inductive limits of symmetric spaces. In…

The notion of the Radon transform on the Heisenberg group was introduced by R. Strichartz and inspired by D. Geller and E.M. Stein's related work. The more general transversal Radon transform integrates functions on the m-dimensional real…

We study horospherical Radon transforms that integrate functions on the $n$-dimensional real hyperbolic space over horospheres of arbitrary fixed dimension $1\le d\le n-1$. Exact existence conditions and new explicit inversion formulas are…

Let S be a non-exceptional oriented surface of finite type. We classify all Radon measures on the space of measured geodesic laminations for S which are invariant under the mapping class group.

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…

We give a definition of Radon hypergeometric function (Radon HGF) of confluent and nonconfluent type, which is a function on the Grassmannian Gr(m,nr) obtained as a Radon transform of a character of the universal covering group of…

We investigate the differentiability properties of real-valued quasiconvex functions f defined on a separable Banach space X. Continuity is only assumed to hold at the points of a dense subset. If so, this subset is automatically residual.…

We prove variable coefficient versions of L^p boundedness results on Hilbert transforms and maximal functions along convex curves in the plane.

Let $ \{X_j, j\in \Z\}$ be a Gaussian stationary sequence having a spectral function $F$ of infinite type. Then for all $n$ and $z\ge 0$,$$ \P\Big\{\sup_{j=1}^n |X_j|\le z \Big\}\le \Big(\int_{-z/\sqrt{G(f)}}^{z/\sqrt{G(f)}}…

Let $\Omega$ be a bounded convex domain in $\mathbb{R}^n$ ($n \ge 2$). In this work, we prove that if there exists an integrable function $f$ such that it's Radon transform over $(n-1)$-dimensional hyperplanes intersecting the domain…

We prove the existence of Rado sets in the Banach space of continuous functions on [0,1]. A countable dense set S is Rado if with probability 1, the infinite geometric random graph on S, formed by probabilistically making adjacent elements…

In $\mathbb{R}^d$, a closed, convex set has zero Lebesgue measure if and only its interior is empty. More generally, in separable, reflexive Banach spaces, closed and convex sets are Haar null if and only if their interior is empty. We…

It is known that if a twice differentiable function has a Lipschitz continuous Hessian, then its gradients satisfy a Jensen-type inequality. In particular, this inequality is Hessian-free in the sense that the Hessian does not actually…

Let G be a real reductive group and G/H a unimodular homogeneous G space with a closed connected subgroup H. We establish estimates for the invariant measure on G/H. Using these, we prove that all smooth vectors in the Banach representation…

We derive a precise link between series expansions of Gaussian random vectors in a Banach space and Parseval frames in their reproducing kernel Hilbert space. The results are applied to pathwise continuous Gaussian processes and a new…

We prove in this short report that for arbitrary weak converging sequence of sigma-finite Borelian measures in the separable Banach space there is a compact embedded separable subspace such that this measures not only are concentrated in…

Novel analysis of finite dimensional Hilbert space is outlined. The approach bypasses general, inherent, difficulties present in handling angular variables in finite dimensional problems: The finite dimensional, d, Hilbert space operators…

We propose an estimator for the mean of random variables in separable real Banach spaces using the empirical characteristic function. Assuming that the covariance operator of the random variable is bounded in a precise sense, we show that…