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G. Lo (1999)
Zero Location and n th Root Asymptotics of Sobolev Orthogonal Polynomials
José Rodríguez (2003)
Approximation by polynomials and smooth functions in Sobolev spaces with respect to measuresJ. Approx. Theory, 120
A. Branquinho, A. Moreno, F. Marcellán (2002)
Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on a Rectifiable Jordan Curve or ArcConstructive Approximation, 18
A. Portilla, Yamilet Quintana, José Rodríguez, E. Tourís (2004)
Weierstrass' theorem with weightsJ. Approx. Theory, 127
A. Moreno, F. Marcellán, K. Pan (1999)
Asymptotic behavior of Sobolev-type orthogonal polynomials on the unit circleJournal of Approximation Theory, 100
A. Iserles, J. Sanz-Serna, P. Koch, S. Nørsett (1990)
Orthogonality and approximation in a Sobolev space
B. Muckenhoupt (1972)
Hardy's inequality with weightsStudia Mathematica, 44
José Rodríguez (2008)
A simple characterization of weighted Sobolev spaces with bounded multiplication operatorJ. Approx. Theory, 153
Mirta Smirnova, Antonio Guardeño (2003)
Boundedness properties for Sobolev inner productsJ. Approx. Theory, 122
G. Lorentz, K. Jetter, S. Riemenschneider (1984)
Birkhoff Interpolation: Introduction
G. Lorentz, K. Jetter, S. Riemenschneider (1984)
Birkhoff Interpolation: Regularity Theorems and Self-Dual Problems
José García, D. Yakubovich (2005)
A Kolmogorov-Szegö-Krein type condition for weighted Sobolev spacesIndiana University Mathematics Journal, 54
A. Cachafeiro, F. Marcellán (1994)
Orthogonal polynomials of Sobolev type on the unit circleJournal of Approximation Theory, 78
A. Iserles, P.E. Koch, S.P. Norsett, J.M. Sanz-Serna (1990)
Algorithms for Approximation
V.G. Maz’ja (1985)
Sobolev Spaces
A. Kufner, B. Opic (1984)
How to define reasonably weighted Sobolev spaces, 25
A. Portilla, Yamilet Quintana, J. Rodríguez, E. Tourís (2007)
Weierstrass's Theorem in Weighted Sobolev Spaces With $k$ DerivativesRocky Mountain Journal of Mathematics, 37
J. Rodríguez (2001)
The Multiplication Operator in Sobolev Spaces with Respect to MeasuresJ. Approx. Theory, 109
A. Portilla, Yamilet Quintana, José Rodríguez, E. Tourís (2007)
Weighted Weierstrass' theorem with first derivativesJournal of Mathematical Analysis and Applications, 334
W. Everitt, L. Littlejohn, S. Williams (1993)
Orthogonal polynomials and approximation in Sobolev spacesJournal of Computational and Applied Mathematics, 48
S. Chua (1996)
On Weighted Sobolev SpacesCanadian Journal of Mathematics, 48
José Rodríguez, Venancio Alvarez, Elena Romera, D. Pestana (2004)
Generalized Weighted Sobolev Spaces and Applications to Sobolev Orthogonal Polynomials IActa Applicandae Mathematica, 80
José Rodríguez, Elena Romera, D. Pestana, Venancio Alvarez (2002)
Generalized weighted Sobolev spaces and applications to Sobolev orthogonal polynomials IIApproximation Theory and its Applications, 18
Venancio Alvarez, D. Pestana, José Rodríguez, Elena Romera (2002)
Weighted Sobolev Spaces on CurvesJ. Approx. Theory, 119
José Rodríguez (2001)
Weierstrass' Theorem in Weighted Sobolev SpacesJ. Approx. Theory, 108
A. Martínez-Finkelshtein (2000)
Bernstein—Szegő's Theorem for Sobolev Orthogonal PolynomialsConstructive Approximation, 16
G. Lagomasino
Sobolev orthogonal polynomials in the complex plane
W.N. Everitt, L.L. Littlejohn, S.C. Williams (1989)
Lecture Notes in Pure and Applied Mathematics
(1984)
Riemenschneider, Birkhoff interpolation
G. Lagomasino, H. Cabrera, I. Izquierdo (2001)
Sobolev orthogonal polynomial in the complex planeJournal of Computational and Applied Mathematics, 127
G. Lagomasino, H. Cabrera (1999)
Zero Location and nth Root Asymptotics of Sobolev Orthogonal PolynomialsJournal of Approximation Theory, 99
A. Iserles, P. Koch, S. Nørsett, J. Sanz-Serna (1991)
On polynomials orthogonal with respect to certain Sobolev inner productsJournal of Approximation Theory, 65
In this paper we obtain some practical criteria to bound the multiplication operator in Sobolev spaces with respect to measures in curves. As a consequence of these results, we characterize the weighted Sobolev spaces with bounded multiplication operator, for a large class of weights. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials. We also obtain some non-trivial results about these Sobolev spaces with respect to measures; in particular, we prove a main result in the theory: they are Banach spaces.
Acta Applicandae Mathematicae – Springer Journals
Published: Jul 8, 2008
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