Solution of the Knaster problem for polynomials of second degree on the two-dimensional sphere
type: Item
instance of: scholarly article
title: Solution of the Knaster problem for polynomials of second degree on the two-dimensional sphere
zbMATH Open document ID: 0814.52004
DOI: 10.1007/BF01208535
author: V. V. Makeev
published in: Mathematical Notes
publication date: 1994-07-12T00:00:00Z
review text: The Knaster problem consists in the determination of configurations \(M\) of points on the sphere \(S^{n - 1} \subset \mathbb{R}^ n\), such that for any continuous function \(f\) on \(S^{n-1}\) there exists a rotation transforming \(M\) into a single level set of \(f\). In this short paper, a variant of the Knaster problem is discussed. It is shown that any four points on a circle \(S \subset S^ 2\) have the described property with respect to functions \(f\) which are polynomials of degree two.
reviewed by: Wolfgang Weil
Mathematics Subject Classification ID: 52A55
Mathematics Subject Classification ID: 26C99
zbMATH DE Number: 567864
zbMATH Keywords: sphere
zbMATH Keywords: point configuration
zbMATH Keywords: polynomial
zbMATH Keywords: Knaster problem
zbMATH Keywords: level set
MaRDI profile type: Publication
cites work: The Topology of Square Pegs in Round Holes
cites work: On a theorem of F. J. Dyson
Recommended article: ON THE SOLUTIONS OF THE SCHWARTZ HOMOGENEOUS PROBLEM IN THE FORM OF VECTOR POLYNOMIALS OF THE SECOND DEGREE
Recommended article: Q4005506
Recommended article: Q4734395
Recommended article: THE KNASTER PROBLEM AND ALMOST SPHERICAL SECTIONS
Recommended article: Polynomial interpolation on the unit sphere. II
Recommended article: On the solutions of the polynomic Laplacian equation
Recommended article: The Krzyz Problem and Polynomials with Zeros on the Unit Circle
Recommended article: Polynomial solutions to Dirichlet problems
Recommended article: Q3211610
Recommended article: Polynomial approximation on spheres - generalizing de la Vallée-Poussin
description: scientific article; zbMATH DE number 567864