A tribute to Géza Freud

We discuss some of the recent work in approximation theory motivated by the research of Geza Freud (1922-1979).

[1]  Paul Nevai.  On orthogonal polynomials , 1979 .

[2]  D. M. Matjila.  Bounds for Lebesgue Functions for Freud Weights , 1994 .

[3]  J. Szabados,et al.  Weighted Lagrange and Hermite–Fejér interpolation on the real line , 1997 .

[4]  Partially one-sided polynomial approxi- mation on the real line , 2001 .

[5]  Steven B. Damelin.  Marcinkiewicz-Zygmund inequalities and the numerical approximation of singular integrals for exponential weights: methods, results and open problems, some new, some old , 2003, J. Complex..

[6]  Hans-Peter Blatt,et al.  Discrepancy of Signed Measures and Polynomial Approximation , 2001 .

[7]  Vilmos Totik,et al.  General Orthogonal Polynomials , 1992 .

[8]  H. Mhaskar.  On the Degree of Approximation in Multivariate Weighted Approximation , 2002 .

[9]  D. Lubinsky,et al.  Quadrature sums and Lagrange interpolation for general exponential weights , 2003 .

[10]  Where Are the Nodes of “Good” Interpolation Polynomials on the Real Line? , 2000 .

[11]  Mean Convergence of Extended Lagrange Interpolation for Exponential Weights , 2003 .

[12]  József Szabados,et al.  Polynomial approximation on infinite intervals with weights having inner zeros , 2002 .

[13]  Vilmos Totik,et al.  Asymptotics for Christoffel Functions with Varying Weights , 2000, Adv. Appl. Math..

[14]  Polynomial Approximation and Interpolation on the Real Line with Respect to General Classes of Weights , 1998 .

[15]  On mean convergence of Hermite–Fejér and Hermite interpolation for Erdős weights , 1998 .

[16]  H. Mhaskar,et al.  A proof of Freud's conjecture for exponential weights , 1988 .

[17]  D. Lubinsky,et al.  (C, 1) Means of Orthonormal Expansions for Exponential Weights , 2000 .

[18]  The Lebesgue Function and Lebesgue Constant of Lagrange Interpolation for Erdoős Weights , 1998 .

[19]  The weighted Lp-norms of orthonormal polynomials for Erdös weights , 1997 .

[20]  Some Erdös-type Convergence Processes in Weighted Interpolation , 2002 .

[21]  Doron S. Lubinsky,et al.  Marcinkiewicz-Zygmund Inequalities: Methods and Results , 1998 .

[22]  Steven B. Damelin,et al.  Asymptotics of recurrence coefficients for orthonormal polynomials on the line - Magnus's method revisited , 2004, Math. Comput..

[23]  J. L. Ullman.  Orthogonal polynomials associated with an infinite interval. , 1980 .

[24]  J. Szabados,et al.  Interpolation of Functions , 1990 .

[25]  Converse Quadrature sum Inequalities for Freud Weights. ii , 2002 .

[26]  P. Vértesi.  On the Lebesgue Function of Weighted Lagrange Interpolation. I. (Freud-Type Weights) , 1999 .

[27]  D. Lubinsky,et al.  L p boundedness of (C, 1) means of orthonormal expansions for general exponential weights , 2002 .

[28]  Song Li.  K-functional, weighted moduli of smoothness, and best weighted polynomial approximation on a simplex , 1999 .

[29]  Hrushikesh Narhar Mhaskar.  On the Representation of Band Limited Functions Using Finitely Many Bits , 2002, J. Complex..

[30]  Converse and Smoothness Theorems for Erdős Weights inL_(0 , 1998 .

[31]  Hrushikesh Narhar Mhaskar,et al.  When is approximation by Gaussian networks necessarily a linear process? , 2004, Neural Networks.

[32]  Hrushikesh Narhar Mhaskar,et al.  Bounded Quasi-Interpolatory Polynomial Operators , 1999 .

[33]  Bounds for weighted Lebesgue functions for exponential weights , 2001 .

[34]  Bounds for weighted Lebesgue functions for exponential weights. II , 2002 .

[35]  D. Lubinsky,et al.  Mean convergence of Lagrange interpolation for Freud's weights with application to product integration rules , 1987 .

[36]  E. Saff,et al.  Logarithmic Potentials with External Fields , 1997 .

[37]  Péter Vértesi,et al.  An Erdős type convergence process in weighted interpolation. II , 2003 .

[38]  T. Kriecherbauer,et al.  Strong asymptotics of polynomials orthogonal with respect to Freud weights , 1999 .

[39]  G. Freud.  On direct and converse theorems in the theory of weighted polynomial approximation , 1972 .

[40]  Hrushikesh Narhar Mhaskar,et al.  Introduction to the theory of weighted polynomial approximation , 1997, Series in approximations and decompositions.

[41]  András Kroó,et al.  On convergent interpolatory polynomials , 1989 .

[42]  C. D. Boor,et al.  Spline approximation by quasiinterpolants , 1973 .

[43]  Péter Vértesi.  On the Lebesgue function of weighted Lagrange interpolation. II , 1998 .

[44]  Mean Convergence of Extended Lagrange Interpolation with Freud Weights , 1999 .

[45]  F. J. Narcowich,et al.  Approximation with interpolatory constraints , 2001 .

[46]  Mean convergence of Hermite-Feje´r and Hermite interpolation for Freud weights , 1998 .

[47]  Hrushikesh Narhar Mhaskar,et al.  Where does the sup norm of a weighted polynomial live? , 1985 .

[48]  The Weighted Lp-Norms of Orthonormal Polynomials for Freud Weights , 1994 .

[49]  David Benko.  Approximation by weighted polynomials , 2003, J. Approx. Theory.

[50]  H. S. Jung.  Linfin convergence of interpolation and associated product integration for exponential weights , 2003, J. Approx. Theory.

[51]  Jackson Theorems for Erdős Weights inLp(0 , 1998 .

[52]  Doron S. Lubinsky,et al.  On Weighted Mean Convergence of Lagrange Interpolation for General Arrays , 2002, J. Approx. Theory.

[53]  Carl de Boor,et al.  The Quasi-Interpolant as a Tool in Elementary Polynomial Spline Theory , 1973 .

[54]  Hrushikesh Narhar Mhaskar,et al.  Extremal problems for polynomials with exponential weights , 1984 .

[55]  Stephanos Venakides,et al.  A Riemann-Hilbert approach to asymptotic questions for orthogonal polynomials , 2001 .

[56]  Convergence of Product Integration Rules for Weights on the Whole Real Line II , 2006 .

[57]  Rene F. Swarttouw,et al.  Orthogonal polynomials , 2020, NIST Handbook of Mathematical Functions.

[58]  Doron S. Lubinsky,et al.  Orthogonal Polynomials for Exponential Weights , 2001 .

[59]  Doron S. Lubinsky,et al.  Orthogonal polynomials for exponential weights x2rhoe-2Q(x) on [0, d) , 2005, J. Approx. Theory.

[60]  C. Chui,et al.  A characterization of multivariate quasi-interpolation formulas and its applications , 1990 .

[61]  P. Vértesi.  AN ERDŐS-TYPE CONVERGENCE PROCESS IN WEIGHTED INTERPOLATION. I, (FREUD-TYPE WEIGHTS) , 2001 .

[62]  D. Lubinsky.  Asymptotics of Orthogonal Polynomials: Some Old, Some New, Some Identities , 2000 .

[63]  Vilmos Totik,et al.  Weighted Approximation with Varying Weight , 1994 .

[64]  Marcel Riesz,et al.  Sur le problme des moments et le thorme de Parseval correspondant , 1924 .

[65]  P. Vértesi,et al.  On Uniform Convergence of Sequences of Certain Linear Operators , 2001 .

[66]  On Some Problems of Weighted Polynomial Approximation and Interpolation , 1999 .

[67]  THE ASYMPTOTIC DISTRIBUTION OF GENERAL INTERPOLATION ARRAYS FOR EXPONENTIAL WEIGHTS , 2002 .

[68]  Steven B. Damelin,et al.  Convergence of Hermite and Hermite-Fejér Interpolation of Higher Order for Freud Weights , 2001, J. Approx. Theory.

[69]  The distribution of zeros of asymptotically extremal polynomials , 1991 .

[70]  Hrushikesh Narhar Mhaskar,et al.  On Marcinkiewicz-Zygmund-Type Inequalities , 1999 .

[71]  H. Mhaskar,et al.  Hermite interpolation at the zeros of certain freud-type orthogonal polynomials , 1992 .