# Search results for: Francisco Marcellán

Journal of Approximation Theory > 2003 > 125 > 1 > 26-41

_{S}=∫fgdμ+λ∫f'g'dμand we characterize the measures μ for which there exists an algebraic relation between the polynomials, {P

_{n}}, orthogonal with respect to the measure μ and the polynomials, {Q

_{n}}, orthogonal with respect to (*), such that the number of involved terms does not depend on the degree of the polynomials...

Journal of Mathematical Analysis and Applications > 2003 > 287 > 1 > 307-319

_{n}} be a sequence of polynomials orthogonal with respect a linear functional u and {Q

_{n}} a sequence of polynomials defined by P

_{n}(x)+s

_{n}P

_{n}

_{-}

_{1}(x)=Q

_{n}(x)+t

_{n}Q

_{n}

_{-}

_{1}(x). We find necessary and sufficient conditions in order to {Q

_{n}} be a sequence of polynomials orthogonal with respect to a linear functional...

Journal of Mathematical Analysis and Applications > 2003 > 283 > 2 > 440-458

_{S}=∫

_{0}

^{~}p(x)q(x)x

^{α}e

^{-}

^{x}dx+λ∫

_{0}

^{~}p'(x)q'(x)dμ(x), where α>-1, λ>=0, and p,q P, the linear space of polynomials with real coefficients. If dμ(x)=x

^{α}e

^{-}

^{x}dx, the corresponding sequence of monic orthogonal polynomials...

Journal of Computational and Applied Mathematics > 2002 > 140 > 1-2 > 159-183

_{μ}(f)=(1/2π)∫02πf(e

^{i}

^{θ})dμ(θ). For this purpose we will construct quadrature formulae which are exact in a certain linear subspace of Laurent polynomials. The zeros of Szego polynomials are chosen as nodes of the corresponding quadratures. We will study...

Linear Algebra and Its Applications > 2001 > 336 > 1-3 > 231-254

Linear Algebra and Its Applications > 2001 > 331 > 1-3 > 155-164

Journal of Computational and Applied Mathematics > 2001 > 127 > 1-2 > 231-254

Journal of Computational and Applied Mathematics > 1997 > 87 > 1 > 87-94

_{n}} denote the sequence of polynomials orthogonal with respect to the Sobolev inner product (f,g)s = ∫0+~ f(x)g(x)x

^{α}e

^{-}

^{x}dx+λ∫0+~ f'(x)g'(x)x

^{α}e

^{-}

^{x}dx where α > - 1, λ > 0 and the leading coefficient of the S

_{n}is equal to the leading coefficient of the Laguerre polynomial L

_{n}

^{(}

^{α}

^{)}. Then, if x Csz[0,+~),...

Journal of Computational and Applied Mathematics > 1997 > 81 > 2 > 217-227

_{n}(x), orthogonal with respect to the inner product (f,g)s = ∫ f(x)g(x)dμ

_{1}(x) + λ ∫ f (x)g (x)dμ

_{2}(x), λ>0, with x outside of the support of the measure μ

_{2}. We assume that μ

_{1}and μ

_{2}are symmetric and compactly supported measures on R satisfying a coherence condition...

Journal of Computational and Applied Mathematics > 1996 > 71 > 2 > 245-265

^{+}

^{[}

^{i}

^{n}

^{f}

^{i}

^{n}

^{]}

_{0}f(x)g(x)x

^{2}e

^{[}

^{m}

^{i}

^{n}

^{u}

^{s}

^{]}

^{x}dx + [lambda] [int ]

^{+}

^{[}

^{i}

^{n}

^{f}

^{i}

^{n}

^{]}

_{0}f[prime ](x)g[prime ](x)x

^{[}

^{a}

^{l}

^{p}

^{h}

^{a}

^{]}...

Journal of Computational and Applied Mathematics > 1995 > 65 > 1-3 > 267-277