RT Journal Article
T1 Rational approximation and Sobolev-type orthogonality
A1 Díaz González, Abel
A1 Pijeira Cabrera, Héctor Esteban
A1 Pérez Yzquierdo, Ignacio
AB In this paper, we study the sequence of orthogonal polynomials {Sn}∞n=0with respect to theSobolev-type inner product⟨ f, g⟩ = ∫ 1−1f (x)g(x) dµ(x) +∑Nj=1η jf(d j)(c j)g(d j)(c j)where µ is a finite positive Borel measure whose support supp (µ) ⊂ [−1, 1] contains an infinite set ofpoints, η j > 0, N, d j ∈ Z+ and {c1, . . . , cN } ⊂ R \ [−1, 1]. Under some restriction of order in thediscrete part of ⟨·, ·⟩, we prove that for sufficiently large n the zeros of Sn are real, simple, n − N ofthem lie on (−1, 1) and each of the mass points c j “attracts” one of the remaining N zeros.The sequences of associated polynomials {S[k]n }∞n=0are defined for each k ∈ Z+. If µ is in the Nevaiclass M(0, 1), we prove an analogue of Markov’s Theorem on rational approximation to Markov typefunctions and prove that convergence takes place with geometric speed.
PB Elsevier
SN 0021-9045
YR 2020
FD 2020-12
LK http://hdl.handle.net/10016/33961
UL http://hdl.handle.net/10016/33961
LA eng
NO Abel Díaz González supported by the Research Fellowship Program, Ministry of Economy and Competitiveness of Spain under grant BES-2016-076613. Héctor Pijeira Cabrera research partially supported by Spanish State Research Agency, under grant PGC2018-096504-B-C33. Ignacio Pérez-Yzquierdo research partially supported by National Fund for Innovation and Scientific and Technological Development (FONDOCyT), Dominican Republic, under grant 2015-1D2-164.
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RD 27 abr. 2024