Let u = {u(t, x); t ∈ [0, T ], x ∈ R} be the process solution of the stochastic heat equation ut = ∆u+ Ḟ , u(0, ·) = 0 driven by a Gaussian noise Ḟ , which is white in time and has spatial covariance induced by the kernel f . In this paper we prove that the process u is locally germ Markov, if f is the Bessel kernel of order α = 2k, k ∈ N+, or f is the Riesz kernel of order α = 4k, k ∈ N+.

We review the relationship between positive operator-valued measures (POVMs) in quantum measurement theory and asymptotic morphisms in the C∗-algebra E-theory of Connes and Higson. The theory of asymptotic spectral measures, as introduced by Martinez and Trout [1], is integrally related to positive asymptotic morphisms on locally compact spaces via an asymptotic Riesz Representation Theorem. Ex...

‎In this note‎, ‎we consider the concentration function problem for a continuous action of a locally compact group $G$ on a locally compact Hausdorff space $X$‎. ‎We prove a necessary and sufficient condition for the concentration functions of a‎ ‎spread-out irreducible probability measure $mu$ on $G$ to converge to zero.

Given a Hilbert space and the generator of a strongly continuous group on this Hilbert space. If the eigenvalues of the generator have a uniform gap, and if the span of the corresponding eigenvectors is dense, then these eigenvectors form a Riesz basis (or unconditional basis) of the Hilbert space. Furthermore, we show that none the conditions can be weakened.

Our purpose here is to announce results in harmonic analysis related to a large class of hypoelliptic operators on arbitrary simply-connected nilpotent Lie groups. We find the asymptotic development of their fundamental solutions, both locally and at infinity, and study corresponding Riesz transforms and analogues of the Hardy-Littlewood-Sobolev theorem for fractional integration. Details will ...

We consider the mixed Dirichlet-conormal problem for heat equation on cylindrical domains with a bounded and Lipschitz base Ω⊂Rd time-dependent separation Λ. Under certain mild regularity assumptions Λ, we show that any q>1 sufficiently close to 1, in Lq is solvable. In other words, given Dirichlet data parabolic Riesz potential space Lq1 Neumann Lq, there unique solution non-tangential maximal...

The phase computation is used in many applications of signal and image processing such as edge, line, symmetry detection, image analysis and recently to show small motion or color changes. Eulerian video processing allows to show small color changes and motions invisibles to the naked eye. Eulerian motion magnification, was modify using the phase and the Riesz pyramid in order to reduce the noi...

We study linear combinations of exponentials en, λn ∈ Λ in the case where the distance between some points λn tends to zero. We suppose that the sequence Λ is a finite union of uniformly discrete sequences. In (Avdonin and Ivanov, 2001), necessary and sufficient conditions were given for the family of divided differences of exponentials to form a Riesz basis in space L(0, T ). Here we prove tha...

This paper deals with the investigation of the computational solutions of a unified fractional reaction-diffusion equation, which is obtained from the standard diffusion equation by replacing the time derivative of first order by the generalized Riemann–Liouville fractional derivative defined by others and the space derivative of second order by the Riesz–Feller fractional derivative and adding...

in this paper, we first introduce some function spaces, with certain locally convex topologies, closely  related to the space of real-valued continuous functions on $x$,  where $x$ is a $c$-distinguished topological space. then, we show that their dual spaces can be identified in a natural way with certain spaces of radon measures.