Christoffel Functions For Power Orthogonal Polynomials

This thesis contains three chapters.In Chapter 1, we introduce some basic concepts and notations needed in the sequel. Furthermore, the background of this thesis is discussed briefly. Then the main results of this thesis are stated as well.In Chapter 2, we give some known results which are the foundations of the results of this thesis, especially, the characteristics and the statements about Christoffel type function for m-orthogonal polynomials.In Chapter 3, this thesis gives the extension of Christoffel function from m-orthogonal polynomials to power orthogonal polynomials. First, we define: For Let polynomial in t satisfies condition: withThen we define the generalized Christoffel function for power orthogonal poly-nomials:Let dμbe a measure on (a, b) and x∈R. The generalized Christoffel functionλj,n+1(dμ,m,m;x) with respect to dμis defined by for and by for respectively, where x is the solution of (1) when j∈Me. Then the existence of this generalize Christoffel function is proved. In addition, its important and interesting characteristics are given. Moreover, some theories concerned with this generalize Christoffel function are given and proved, particularly, we show that under some provided cases there is a unique vector x∈Xpq satisfies...