Result: Orthogonal polynomials of equilibrium measures supported on Cantor sets

Title:
Orthogonal polynomials of equilibrium measures supported on Cantor sets
Authors:
MANTICA, GIORGIO DOMENICO PIO
Source:
Journal of Computational and Applied Mathematics. 290:239-258
Publication Status:
Preprint
Publisher Information:
Elsevier BV, 2015.
Publication Year:
2015
Subject Terms:
Jacobi (tridiagonal) operators (matrices) and generalizations, Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions, iterated function systems, FOS: Physical sciences, 42C05 (Primary) 31A15, 47B36, 81Q10, 30C30 (Secondary), 01 natural sciences, potential theory, FOS: Mathematics, Mathematics - Numerical Analysis, Complex Variables (math.CV), 0101 mathematics, Almost periodic Jacobi matrices, Conformal mapping, Equilibrium measure, Iterated Function systems, Orthogonal polynomials, Potential theory, Computational Mathematics, Applied Mathematics, Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis, orthogonal polynomials, Mathematical Physics, Selfadjoint operator theory in quantum theory, including spectral analysis, 2. Zero hunger, Quantum Physics, conformal mapping, Mathematics - Complex Variables, Numerical Analysis (math.NA), Mathematical Physics (math-ph), Schwarz-Christoffel-type mappings, almost periodic Jacobi matrices, Quantum Physics (quant-ph), equilibrium measure
Document Type:
Academic journal Article
File Description:
application/xml
Language:
English
ISSN:
0377-0427
DOI:
10.1016/j.cam.2015.05.014
DOI:
10.48550/arxiv.1311.4819
Access URL:
http://arxiv.org/abs/1311.4819
https://zbmath.org/6473779
https://doi.org/10.1016/j.cam.2015.05.014
https://arxiv.org/abs/1311.4819
http://ui.adsabs.harvard.edu/abs/2013arXiv1311.4819M/abstract
https://core.ac.uk/display/53563512
https://dialnet.unirioja.es/servlet/articulo?codigo=5282553
https://arxiv.org/pdf/1311.4819v1
https://dblp.uni-trier.de/db/journals/jcam/jcam290.html#Mantica15
Rights:
Elsevier Non-Commercial
arXiv Non-Exclusive Distribution
Accession Number:
edsair.doi.dedup.....a54a9f971a8e8384fef4d19913aa75d9
Database:
OpenAIRE

Further Information

We study the orthogonal polynomials associated with the equilibrium measure, in logarithmic potential theory, living on the attractor of an Iterated Function System. We construct sequences of discrete measures, that converge weakly to the equilibrium measure, and we compute their Jacobi matrices via standard procedures, suitably enhanced for the scope. Numerical estimates of the convergence rate to the limit Jacobi matrix are provided, that show stability and efficiency of the whole procedure. As a secondary result, we also compute Jacobi matrices of equilibrium measures on finite sets of intervals, and of balanced measures of Iterated Function Systems. These algorithms can reach large orders: we study the asymptotic behavior of the orthogonal polynomials and we show that they can be used to efficiently compute Green's functions and conformal mappings of interest in constructive function theory.
28 pages, 15 figures