Orthogonal polynomials on Sobolev spaces: old and new directions

Pseudo-uniform Convexity in Hp and Some Extremal Problems on Sobolev Spaces

“…In the case p ¼ 2, the polynomials fP n g n¼0, 1,... are usually said to be Sobolev orthogonal polynomials. The special case k ¼ 1 has been studied by many authors (see, for instance [10,12,18]). For k ¼ 0 we have the classical orthogonality.…”

Orthogonal polynomials

“…Perhaps the most natural one is smooth data fitting. The Spanish school around F. Marcellán, G. Lopez and A. Martinez-Finkelshtein has been particularly active in developing this area (see the surveys Marcellán-Alfaro-Rezola [51] and Martinez-Finkelshtein [53,52] and the references therein). In this section let Q n (z) = z n + · · · denote the monic orthogonal polynomial with respect to the Sobolev inner product (13.1), and q n (µ k ) the monic orthogonal polynomials with respect to the measure µ k .…”

Asymptotics for Sobolev Orthogonal Polynomials for Exponential Weights

“…(3) Sobolev orthogonal polynomials have found application in a number of contexts. See, for instance, the survey papers [19], [23], as well as [16]. In particular in [13], a study of Fourier series of Sobolev orthogonal polynomials was initiated for smooth functions.…”