Zeros of Sobolev Orthogonal Polynomials via Muckenhoupt Inequality with Three Measures

Iterated integrals and Borwein-Chen-Dilcher polynomials

“…There are several papers on this issue (e.g. [1,2,8,9,12,14]). These polynomials are useful in Fourier analysis ( [5,14]), numerical analysis ( [6]), and so on (see [9] and references therein).…”

Iterated Integrals and Borwein–Chen–Dilcher Polynomials

“…There are several papers on this issue (e.g. [1,2,7,8,11,13]). These polynomials are useful in Fourier analysis [13], numerical analysis [5], and so on (see [8] and references therein).…”

Concerning Asymptotic Behavior for Extremal Polynomials Associated to Nondiagonal Sobolev Norms

“…In [1] the authors obtain the th root asymptotic of Sobolev orthogonal polynomials when the zeros of these polynomials are contained in a compact set of the complex plane; however, the boundedness of the zeros of Sobolev orthogonal polynomials is an open problem, but as was stated in [2], it could be obtained as a consequence of the boundedness of the multiplication operator ( ) = ( ). Thus, finding conditions to ensure the boundedness of would provide important information about the crucial issue of determining the asymptotic behavior of Sobolev orthogonal polynomials (see, e.g., [3][4][5][6][7][8][9][10][11][12][13]). The more general result on this topic is [ (1) (see Theorem 3 below, which is [3,Theorem 8.1] in the case = 1).…”