On polynomials orthogonal to all powers of a given polynomial on a segment
Copyright policy )On polynomials orthogonal to all powers of a given polynomial on a segment
In this paper we investigate the following "polynomial moment problem": for a complex polynomial $P(z)$ and distinct complex numbers $a,b$ to describe polynomials $q(z)$ orthogonal to all integer non-negative powers of $P(z)$ on the segment $[a,b].$
27 pages, 9 figures
Moments, Algebraic functions, Mathematics(all), Cauchy type integrals, Mathematics - Complex Variables, Cauchy-type intergrals, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Polynomials, polynomial moment problem, Galois groups, orthogonality, Mathematics - Classical Analysis and ODEs, Polynomials and rational functions of one complex variable, algebraic functions, Center problem, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Cacti, Orthogonality, Complex Variables (math.CV), Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
Moments, Algebraic functions, Mathematics(all), Cauchy type integrals, Mathematics - Complex Variables, Cauchy-type intergrals, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, Polynomials, polynomial moment problem, Galois groups, orthogonality, Mathematics - Classical Analysis and ODEs, Polynomials and rational functions of one complex variable, algebraic functions, Center problem, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Cacti, Orthogonality, Complex Variables (math.CV), Integration, integrals of Cauchy type, integral representations of analytic functions in the complex plane
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