Related papers: On the Gauss-Kuzmin-L\'evy problem for nearest int…

A theory of intermittency differentiation is developed for a general class of Gaussian Multiplicative Chaos measures including the measure of Bacry and Muzy on the interval and circle as special cases. An exact, non-local functional…

We study a class of Wilsonian formulations of non-Abelian gauge theories in algebraic non-covariant gauges where the Wilsonian infrared cutoff $\Lambda$ is inserted as a mass term for the propagating fields. In this way the Ward-Takahashi…

Let $(X,\mathcal{A}, \mu)$ be a probability measure space and let $T_i,$ $1\leq i\leq H,$ be commuting invertible measure preserving transformations on this measure space. We prove the following pointwise results; The averages…

In this article, we study a model problem featuring a L\'evy process in a domain with semi-transparent boundary by considering the following perturbed fractional Laplacian operator \[\mathscr{L}_{b,q} := (-\Delta)^t +…

Let $\lambda_1(n)$ denote the least invariant factor in the invariant factor decomposition of the multiplicative group $M_n = (\mathbb Z/n\mathbb Z)^\times$. We give an asymptotic formula, with order of magnitude $x/\sqrt{\log x}$, for the…

Using lattice approximations of Euclidean space, we develop a way to approximate stable processes that are represented by stochastic integrals over Euclidean space. Via a stable version of the Lindeberg-Feller Theorem we show that the…

The Gr\"unwald and shifted Gr\"unwald formulas for the function $y(x)-y(b)$ are first order approximations for the Caputo fractional derivative of the function $y(x)$ with lower limit at the point $b$. We obtain second and third order…

We consider a parabolic equation in a bounded domain $\OOO$ over a time interval $(0,T)$ with the homogeneous Neumann boundary condition. We arbitrarily choose a subboundary $\Gamma \subset \ppp\OOO$. Then, we discuss an inverse problem of…

We consider linear and non-linear boundary value problems associated to the fractional Hardy-Schr\"odinger operator $ L_{\gamma,\alpha}: = ({-}{ \Delta})^{\frac{\alpha}{2}}- \frac{\gamma}{|x|^{\alpha}}$ on domains of $\mathbb{R}^n$…

This article provides optimal constants for two quantitative recurrence problems. First of all for recurrence of maps of the interval [0,1] that preserve the Lebesgue measure and on the other hand Lagrange spectrum of interval exchange…

We consider the asymptotic expansion of the Mathieu-Bessel series \[S_{\nu,\gamma}^{\mu}(a,b)=\sum_{n=1}^\infty \frac{n^\gamma K_\nu(nb/a)}{(n^2+a^2)^\mu}, \qquad (\mu>0, \nu\geq 0, b>0, \gamma\in {\bf R})\] as $|a|\to\infty$ in…

We study the properties of reflectionless measures for a Calder\'{o}n-Zygmund operator T. Roughly speaking, these are measures $\mu$ for which T(\mu) vanishes (in a weak sense) on the support of the measure. We describe the relationship…

Let $G$ be a reductive algebraic group over $\mathbb{Q}$ and $\Gamma\subset G(\mathbb{Q})$ an arithmetic subgroup. Let $K_\infty\subset G(\mathbb{R})$ be a maximal compact subgroup. We study the asymptotic behavior of the counting functions…

We provide explicit ranges for $\sigma$ for which the asymptotic formula \begin{equation*} \int_0^T|\zeta(1/2+it)|^4|\zeta(\sigma+it)|^{2j}dt \;\sim\; T\sum_{k=0}^4a_{k,j}(\sigma)\log^k T \quad(j\in\mathbb N) \end{equation*} holds as…

As a consequence of the main result of this paper efficient conditions guaranteeing the existence of a $T-$periodic solution to the second order differential equation \begin{equation*} u"=\frac{h(t)}{u^{\lambda}} \end{equation*} are…

We prove a Burgess-like subconvex bound for twisted L-functions of a fixed irreducible cuspidal automorphic representation of GL(2) over a totally real number field. The proof is based on a spectral decomposition of shifted convolution sums…

We study dynamic minimization problems of the calculus of variations with generalized Lagrangian functionals that depend on a general linear operator $K$ and defined on bounded-time intervals. Under assumptions of regularity, convexity and…

In this paper we continue investigation of the interior problem of tomography that was started in \cite{BKT2}. As is known, solving the interior problem {with prior data specified on a finite collection of intervals $I_i$} is equivalent to…

The results of Koml\'{o}s, Major and Tusn\'{a}dy give optimal Wiener approximation of partial sums of i.i.d. random variables and provide an extremely powerful tool in probability and statistical inference. Recently Wu [Ann. Probab. 35…

Summary]{In this paper, we study problems of minimization of a functional depending on the fractional Caputo derivative of order $0<\alpha \leq 1$ and the fractional Riemann- Liouville integral of order $\beta > 0$ at fixed endpoints. A…