Related papers: Complex Tauberian theorems for Laplace transforms …
The paper provides new upper and lower bounds for the multivariate Laplace approximation under weak local assumptions. Their range of validity is also given. An application to an integral arising in the extension of the Dixon's identity is…
We present a construction of harmonic functions on bounded domains for the spectral fractional Laplacian operator and we classify them in terms of their divergent profile at the boundary. This is used to establish and solve boundary value…
We extend the well-known Katznelson-Tzafriri theorem, originally posed for power-bounded operators, to the case of Ces\`aro bounded operators of any order $\alpha>0.$ For this purpose, we use a functional calculus between a new class of…
We establish the transition behavior of Jacquet-Whittaker functions on split semi-simple Lie groups. As a consequence, we show that for certain finite volume Riemannian manifolds, the local bound for normalized Laplace eigenfunctions does…
We prove variants of Wiener's Tauberian theorem in the framework of quantum harmonic analysis, i.e. for convolutions between an absolutely integrable function and a trace class operator, or of two trace class operators. Our results include…
We present a systematic study on a class of nonlocal integral functionals for functions defined on a bounded domain and the naturally induced function spaces. The function spaces are equipped with a seminorm depending on finite differences…
This paper extends two recent improvements in the Hilbert space setting of the well-known Katznelson-Tzafriri theorem by establishing both a version of the result valid for bounded representations of a large class of abelian semigroups and…
We develop a new technique for studying the boundary limiting behavior of a holomorphic function on a domain $\Omega$ -- both in one and several complex variables. The approach involves two new localized maximal functions. As a result of…
It has been empirically observed that eigenfunctions of Laplace's equation $-\Delta \phi = \lambda \phi$ with Neumann boundary conditions sometimes localize near the boundary of the domain if that boundary is rough (say, fractal). This has…
This paper surveys Abelian and Tauberian theorems for long-range dependent random fields. We describe a framework for asymptotic behaviour of covariance functions or variances of averaged functionals of random fields at infinity and…
We prove a Tauberian theorem for the Laplace--Stieltjes transform and Karamata-type theorems in the framework of regularly log-periodic functions. As an application we determine the exact tail behavior of fixed points of certain type…
We extend the classical Titchmarsh theorems to the Fourier transform of two types of H\"older-Lipschitz functions - additive and multiplicative - defined on fundamental domains of lattices in $\mathbb{R}^d$. Our approach is based on…
We give a detailed exposition of the proof of Richter's local limit theorem in a refined form, and establish the stability of the remainder term in this theorem under small perturbations of the underlying distribution (including smoothing).…
We consider the three-dimensional incompressible free-boundary Euler equations in a bounded domain and with surface tension. Using Lagrangian coordinates, we establish a priori estimates for solutions with minimal regularity assumptions on…
The analytic continuation to an imaginary velocity of the canonical partition function of a thermal system expressed in a moving frame has a natural implementation in the Euclidean path-integral formulation in terms of shifted boundary…
The Virasoro minimal models with boundary are described in the Landau-Ginzburg theory by introducing a boundary potential, function of the boundary field value. The ground state field configurations become non-trivial and are found to obey…
It is developed the theory of the boundary behavior of homeomorphic solutions of the Beltrami equations ${\bar{\partial}}f=\mu\,{\partial}f$ of the Sobolev class $W^{1,1}_{\rm loc}$ with respect to prime ends of domains. On this basis,…
Traditional approaches to energy-momentum localization led to reference frame dependent pseudotensors. The more modern idea is quasilocal energy-momentum. We take a Hamiltonian approach. The Hamiltonian boundary term gives not only the…
We study the asymptotic behaviour of a properly normalized time changed Wiener processes. The time change reflects the fact that we consider the Laplace operator (which generates a Wiener process) multiplied by a possibly degenerate…
We give a parameter version of Graham-Kerzman approximation theorem for bounded holomorphic functions on strictly pseudoconvex domains. As an application, we present some uniform estimates for the boundary behaviour of the Kobayashi and…