Fox, Daniel J. F.
Published in
Analysis and Mathematical Physics

There is considered the problem of describing up to linear conformal equivalence those harmonic cubic homogeneous polynomials for which the squared-norm of the Hessian is a nonzero multiple of the quadratic form defining the Euclidean metric. Solutions are constructed in all dimensions and solutions are classified in dimension at most 4. Techniques...

Piorkowski, Mateusz Teschl, Gerald
Published in
Analysis and Mathematical Physics

We take a closer look at the Riemann–Hilbert problem associated to one-gap solutions of the Korteweg–de Vries equation. To gain more insight, we reformulate it as a scalar Riemann–Hilbert problem on the torus. This enables us to derive deductively the model vector-valued and singular matrix-valued solutions in terms of Jacobi theta functions. We co...

Gustafsson, Björn
Published in
Analysis and Mathematical Physics

The author, who was a student and colleague of Harold S. Shapiro, gives some personal memories from Shapiro’s time as a professor at KTH, Stockholm, 1972-2021.

Kraus, Daniela Moucha, Annika Roth, Oliver
Published in
Analysis and Mathematical Physics

We prove a sharp Bernstein-type inequality for complex polynomials which are positive and satisfy a polynomial growth condition on the positive real axis. This leads to an improved upper estimate in the recent work of Culiuc and Treil (Int. Math. Res. Not. 2019: 3301–3312, 2019) on the weighted martingale Carleson embedding theorem with matrix weig...

Bögli, Sabine Kennedy, James B. Lang, Robin
Published in
Analysis and Mathematical Physics

We study the spectrum of the Robin Laplacian with a complex Robin parameter α\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\alpha $$\end{document} on a bounded Lipsch...

Gardiner, Stephen J. Sjödin, Tomas
Published in
Analysis and Mathematical Physics

Gustafsson and Lin recently published a significant result concerning Laplacian growth problems that start from a simply connected planar domain. However, the validity of their result depends on the verification of a particular conjecture. This paper provides the missing proof.

Friedman, Yaakov Peralta, Antonio M.
Published in
Analysis and Mathematical Physics

There are six different mathematical formulations of the symmetry group in quantum mechanics, among them the set of pure states P\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{do...

Nunokawa, Mamoru Sokół, Janusz
Published in
Analysis and Mathematical Physics

Jack’s Lemma says that if f(z) is regular in the disc |z|≤r\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$|z|\le r$$\end{document}, f(0)=0\documentclass[12pt]{minimal}...

Lemm, Marius Sutter, David
Published in
Analysis and Mathematical Physics

Lyapunov exponents characterize the asymptotic behavior of long matrix products. In this work we introduce a new technique that yields quantitative lower bounds on the top Lyapunov exponent in terms of an efficiently computable matrix sum in ergodic situations. Our approach rests on two results from matrix analysis—the n-matrix extension of the Gol...

Gupta, Preeti Hans, Sunil Mir, Abdullah
Published in
Analysis and Mathematical Physics

The main purpose of this paper is to established the modulus of derivative of rational functions r(z) having all its zeros in |z|≤k≤1,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \beg...