| Full text | |
| Author(s): |
Ranga, A. Sri
Total Authors: 1
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| Document type: | Journal article |
| Source: | Proceedings of the American Mathematical Society; v. 144, n. 3, p. 1129-1143, MAR 2016. |
| Web of Science Citations: | 1 |
| Abstract | |
The principal objective here is to look at some algebraic properties of the orthogonal polynomials Psi((b,s,t))(n) with respect to the Sobolev inner product on the unit circle < f, g >(S(b,s,t)) = (1 - t) < f, g >(mu(b)) + t <(f(1))over bar> g(1) + s < f', g'>(mu(b+1)) where < f, g >(mu(b)) - tau(b)/2 pi integral(2 pi)(0) f(e(i theta))g(e(i theta)) (e(pi-theta))(Im(b)) (sin(2)(theta/2))(Re(b))d theta. Here, Re(b) > -1/2, 0 <= t < 1, s > 0 and tau(b) is taken to be such that < 1, 1 >(mu(b)) = 1. We show that, for example, the monic Sobolev orthogonal polynomials. Psi n((b,s,t)) satisfy the recurrence Psi n((b,s,t)) (z)-beta n((b,s,t)) Psi((b,s,t))(n-1) (z) = Phi((b,s,t))(n) (z) n >= 1, where Psi((b,s,t))(n) are the monic orthogonal polynomials with respect to the inner product < f, g >(S(b,s,t)) = (1 - t) < f, g >(mu(b)) + t <(f(1))over bar> g(1). Some related bounds and asymptotic properties are also given. (AU) | |
| FAPESP's process: | 09/13832-9 - Orthogonal polynomials, special functions and applications |
| Grantee: | Dimitar Kolev Dimitrov |
| Support Opportunities: | Research Projects - Thematic Grants |