相关论文: Note on the Dirichlet Approximation Theorem

In this paper we survey many results on the Dirichlet space of analytic functions. Our focus is more on the classical Dirichlet space on the disc and not the potential generalizations to other domains or several variables. Additionally, we…

We prove an analogue of the classical Bernstein theorem concerning the rate of polynomial approximation of piecewise analytic functions on a compact subset of the real line.

Based on a generalization of Bohr's equivalence relation for general Dirichlet series, in this paper we study the sets of values taken by certain classes of equivalent almost periodic functions in their strips of almost periodicity. In…

I review the classical theory of likelihood based inference and consider how it is being extended and developed for use in complex models and sampling schemes.

A complete p-adic Khintchine type theorem for approximation by p-adic algebraic numbers is established.

Approximation in measure is employed to solve an asymptotic Dirichlet problem on arbitrary open sets and to show that many functions, including the Riemann zeta-function, are universal in measure. Connections with the Riemann Hypothesis are…

We consider a sum of the derivatives of Dirichlet $L$-functions over the zeros of Dirichlet $L$-functions. We give an asymptotic formula for the sum.

We consider the boundary value problem associated to the divergence operator with vanishing Dirichlet boundary conditions and we prove the existence of classical solutions under slight assumptions on the regularity of the datum.

In this article we shall go over recent work in proving dispersive and Strichartz estimates for the Dirichlet-wave equation. We shall discuss applications to existence questions outside of obstacles and discuss open problems.

A classical probabilistic explanation for Hardy's quantum paradox is demonstrated.

We prove the existence of classical solutions to the Dirichlet problem for a class of fully nonlinear elliptic equations of curvature type on Riemannian manifolds. We also derive new second derivative boundary estimates which allows us to…

The Dirichlet divisor problem is used as a model to give a conjecture concerning the conditional convergence of the Dirichlet series of an L-function.

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

We present other proofs, generalizations and analogues of the identities concerning multiple Dirichlet series by Tahmi and Derbal (2022). As applications, we obtain asymptotic formulas with remainder terms for certain related sums.

In this note we prove a converse of Bohr's equivalence theorem for Dirichlet series under some natural assumptions.

The Dirichlet form is a generalization of the Laplacian, heavily used in the study of many diffusion-like processes. In this paper we present a nonstandard representation theorem for the Dirichlet form, showing that the usual Dirichlet form…

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

The paper is mostly a survey on recent results in Diophantine approximation, with emphasis on properties of exponents measuring various notions of Diophantine <approximation.

We solve the Dirichlet problem in the unit disc and derive the Poisson formula using very elementary methods and explore consequent simplifications in other foundational areas of complex analysis.

We introduce methods that allow to derive continuous-time versions of various discrete-time ergodic theorems. We then illustrate these methods by giving simple proofs and refinements of some known results as well as establishing new results…