Linear Holomorphic Partial Differential Equations and Classical Potential Theory

  title={Linear Holomorphic Partial Differential
 Equations and Classical Potential Theory},
  author={Dmitry Khavinson and Erik Lundberg},
  journal={Mathematical Surveys and

Point source equilibrium problems with connections to weighted quadrature domains

Inradius of random lemniscates

A BSTRACT . A classically studied geometric property associated to a complex polynomial p is the inradius (the radius of the largest inscribed disk) of its (filled) lemniscate Λ := { z ∈ C : | p ( z )

Fischer decompositions for entire functions and the Dirichlet problem for parabolas

Let P2k\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek}

Bitensorial formulation of the singularity method for Stokes flows

This paper develops the bitensorial formulation of the system of singularities associated with unbounded and bounded Stokes flows. The motivation for this extension is that Stokesian singularities

Harold Seymour Shapiro 1928–2021; Life in mathematics, in memoriam

This is a (very) personal outlook on the life and mathematical achievements of Harold S. Shapiro, who has passed away in March of 2021, a few days short of his 93rd birthday. It is based on the

Holomorphic solutions of soliton equations

  • A. Domrin
  • Mathematics
    Transactions of the Moscow Mathematical Society
  • 2022
We present a holomorphic version of the inverse scattering method for soliton equations of parabolic type in two-dimensional space-time. It enables one to construct examples of solutions holomorphic

Extension theorems for harmonic functions which vanish on a subset of a cylindrical surface

Probabilistic bounds on best rank-one approximation ratio

We provide new upper and lower bounds on the minimum possible ratio of the spectral and Frobenius norms of a (partially) symmetric tensor. In the particular case of general tensors our result

Harmonic extension through conical surfaces

This paper establishes extension results for harmonic functions which vanish on a conical surface. These are based on a detailed analysis of expansions for the Green function of an infinite cone.


A theorem of nehari revisited

A well-known theorem of Z. Nehari shows how one can locate the singular points of a function f(z) given by where p n(z) is the Legendre polynomial of degree n, by relating them to the singular points