Recent Progress in Polyhedral Harmonics

Keywords

Mathematics, Property (philosophy), Polytope, Algebra over a field, Curse of dimensionality

References

Lectures on topics in mean periodic functions and the two-radius theoremJean Delsarte, K. B. Vedak — 1961
Fourier analysis in several complex variablesLeon Ehrenpreis — 1970
Invariants of Finite Reflection GroupsLouis Solomon — 1963
Four different unknown functions satisfying the triangle mean value property for harmonic polynomials, IIShigeru Haruki — 1977
Mean values and differential equationsLawrence Zalcman — 1973
On two functional equations connected with a mean-value property of polynomialsShigeru Haruki — 1971
On the mean value property of harmonic and complex polynomialsShigeru Haruki — 1981
Remarks on a paper by A. Friedman.Maxwell O. Reade — 1957
Partial Differential Equations and Difference EquationsLeopold Flatto — 1965
A new look at interpolation theory for entire functions of one variableCarlos A. Berenstein, B. A. Taylor — 1979
Averaging sets: A generalization of mean values and spherical designsPaul Seymour, Thomas Zasĺavsky — 1984
The converse of Gauss's theorem for harmonic functionsLeopold Flatto — 1965
A note on the mean value propertyAdriano M. Garsia — 1962
Mean-values and harmonic polynomialsE. F. Beckenbach, Maxwell O. Reade — 1943
Boundedness on a set of positive measure and the mean value property characterizes polynomials on a spaceVnM. A. McKiernan — 1968
Regular solids and harmonic polynomialsE. F. Beckenbach, Maxwell O. Reade — 1945
Polytopes and the mean value propertyKazuhiro Iwasaki — 1997
Mean-values and polyharmonic polynomials.Avner Friedman — 1957
General and regular solutions of functional equations characterizing harmonic polynomialsJ. Aczél, Hiroshi Haruki, M. A. McKiernan — 1968
On polynomials characterized by a certain mean value propertyLeopold Flatto — 1966

Cited by

Canonical Systems of Basic Invariants for Unitary Reflection GroupsNorihiro Nakashima, Hiroaki Terao, Shuhei Tsujie — 2013
Searching for integrable Hamiltonian systems with Platonic symmetriesGiovanni Rastelli — 2010
Polynomial Invariants and Harmonic Functions Related to Exceptional Regular PolytopesKatsunori Iwasaki, Atsufumi Kenma, Keiji Matsumoto — 2002
Cubic harmonics and Bernoulli numbersKatsunori Iwasaki — 2011
多面体調和関数の数理-多面体・不変式・偏微分方程式岩崎克則 — 2002
On a polygonal mean value propertyGrzegorz Łysik — 2022

Related papers

Computing The Extension Complexities of All 4-Dimensional 0/1-PolytopesMichael L. Oelze, Arnaud Vandaele, Stefan Weltge — 2014
Ehrhart Polynomial Roots of Reflexive PolytopesGábor Hegedüs, Akihiro Higashitani, Alexander Kasprzyk — 2015
Thin polytopes: Lattice polytopes with vanishing local h^*-polynomialChristopher Borger, A. Kretschmer, Benjamin Nill — 2022
Computing Entanglement PolytopesKonstantin Wernli — 2018
Thin Polytopes: Lattice Polytopes With Vanishing Local h*-PolynomialChristopher Borger, A. Kretschmer, Benjamin Nill — 2023
Affine subspace concentration conditions for centered polytopesAnsgar Freyer, Martin Henk, Christian Kipp — 2022
2-levelness of Marked Poset Polytopes and the Ehrhart polynomialJan Stricker — 2024