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Control variates have seen recent interest as a powerful technique to reduce the variance of summary statistics measured from costly cosmological $N$-body simulations. Of particular interest are the class of control variates which are…

We prove that if $K$ is a compact space and the space $P(K\times K)$ of regular probability measures on $K\times K$ has countable tightness in its $weak^*$ topology, then $L_1(\mu)$ is separable for every $\mu\in P(K)$. It has been known…

In this paper, we study the exact boundary controllability of the linear fourth-order Schr\"odinger equation, with variable physical parameters and clamped boundary conditions on a bounded interval. The control acts on the first spatial…

Being motivated by the famous Kaplansky theorem we study various sequential properties of a Banach space $E$ and its closed unit ball $B$, both endowed with the weak topology of $E$. We show that $B$ has the Pytkeev property if and only if…

The existence of continuous not necessarily bounded solutions of nonlinear functional Volterra integral inclusions in infinite dimensional setting is shown with the aid of the measure of nonequicontinuity. New abstract topological fixed…

In this work we provide a geometric characterization of the measures $\mu$ in $\mathbb R^{n+1}$ with polynomial upper growth of degree $n$ such that the $n$-dimensional Riesz transform $R\mu (x) = \int \frac{x-y}{|x-y|^{n+1}}\,d\mu(y)$…

We prove a Leibniz rule for BV functions in a complete metric space that is equipped with a doubling measure and supports a Poincar\'e inequality. Unlike in previous versions of the rule, we do not assume the functions to be locally…

We consider the Benjamin-Bona-Mahony (BBM) equation on the one dimensional torus T = R/(2{\pi}Z). We prove a Unique Continuation Property (UCP) for small data in H^1(T) with nonnegative zero means. Next we extend the UCP to certain BBM-like…

Let $X$ be a separable Banach space endowed with a non-degenerate centered Gaussian measure $\mu$ and let $w$ be a positive function on $X$ such that $w\in W^{1,s}(X,\mu)$ and $\log w\in W^{1,t}(X,\mu)$ for some $s>1$ and $t>s'$. In the…

Let $G = (V,E)$ be a connected graph. A probability measure $\mu$ on $V$ is called "balanced" if it has the following property: if $T_\mu(v)$ denotes the "earth mover's" cost of transporting all the mass of $\mu$ from all over the graph to…

We define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space. We study both the projective…

We introduce a multivariate Markov transform which generalizes the well-known one-dimensional Stieltjes transform from the Moment problem and Spectral theory. Our main result states that two measures {\mu} and {\nu} with bounded support…

This paper is the first part of a project devoted to studying the interconnection between controllability properties of a dynamical system and the large-time asymptotics of trajectories for the associated stochastic system. It is proved…

We study an optimal control problem of McKean--Vlasov branching diffusion processes, in which the interaction term is determined by the marginal measure induced by all alive particles in the system. Accordingly, the value function is…

Let $(T,{\cal F},\mu)$ be a $\sigma$-finite measure space, $E$ a separable real Banach space and $p\geq 1$. Given a sequence of functions $f, f_1, f_2,...$ from $T\times E$ to ${\bf R}$, under general assumptions, we prove that, for each…

Let $L$ be a holomorphic line bundle on a compact complex manifold $X$ of dimension $n,$ and let $e^{-\phi}$ be a continuous metric on $L.$ Fixing a measure $d\mu$ on $X$ gives a sequence of Hilbert spaces consisting of holomorphic sections…

We show that the {\alpha}-fractional Bilinear Indicator/Cube Testing Constant arising in arXiv:1906.05602 is controlled by the classical fractional Muckenhoupt constant, provided the product measure {\sigma} x {\omega} is diagonally reverse…

This paper introduces the formalism required to analyze a certain class of stochastic control problems that involve a super diffusion as the underlying controlled system. To establish the existence of these processes, we show that they are…

Mockenhaupt and Tao (Duke 2004) proved a finite field analogue of the Stein--Tomas restriction theorem, establishing a range of $q$ for which $L^q\to L^2$ restriction estimates hold for a given measure $\mu$ on a vector space over a finite…

This paper mainly establishes the finite-horizon stochastic bounded real lemma, and then solves the $H_{\infty}$ control problem for discrete-time stochastic linear systems defined on the separable Hilbert spaces, thereby unifying the…