Problems in approximation theory. Classical and weighted cases.  Page description

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Details of project

  
Identifier
37299
Type K
Principal investigator Vértesi, Péter
Title in Hungarian Approximációelméleti kérdések. Klasszikus és súlyozott eset.
Title in English Problems in approximation theory. Classical and weighted cases.
Panel Mathematics and Computing Science
Department or equivalent Alfréd Rényi Institute of Mathematics
Participants Gróf, József
Gyorvári, János
Hermann, Tamás
Szabados, József
Starting date 2002-01-01
Closing date 2006-12-31
Funding (in million HUF) 9.971
FTE (full time equivalent) 0.00
state closed project





 

Final report

  
Results in Hungarian
Az Erdos Pál és Freud Géza által kezdeményezett súlyozott approximáció vizsgálata véges és végtelen intervallumon. Konvergens eljárások (interpolációs - és Fourier soros ) konstruálása különbözo súlyok esetén, véges és végtelen intervallumon,elsösorban Jacobi -illetve Laguerre típusú súlyok esetén.melyek esetleg belső szingularitással is birnak. Szász -Mirakjan féle operátorok vizsgálata a számegyenesen.Alkalmazások. Bernstein- Jackson tipusú problémák vizsgálata több változós esetben,különféle tartományokon.
Results in English
The main areas are as follows: Weighted approximation on the real line and on finite interval based on some problems initiated by Pál Erdős and Géza Freud. Construction of convergent processes (interpolatory and Fourier series-type) using different weights,on finite and infinite intervals, based on Jacobi- and Laguerre type weights. We investigated the so called Szász-Mirakjan operators on the real line. We obtained convergence results improving some previously obtained conditions. Some applications were proved,too. We investigated some Bernstein and Jackson type problems for the multidimensional cases on different domains.
Full text http://real.mtak.hu/152/
Decision
Yes





 

List of publications

  
Szabados, J.: Orthogonal polynomials, A Panorama of Hungarian Mathematics in the Twentieth Century I., Bolyai Society Mathematical Studies, Vol.14, Springer, (2005), 55-71., 2005
Benko D; Erdélyi T; Szabados J: The full Markov--Newman inequality for Müntz polynomials on positive intervals, Proc. Amer. Math. Soc. 131: pp. 2385-2391, 2003
Szili L; Vértesi P: On summability of weighted Lagrange interpolation. I, Acta Math. Hugar. 101: 323-344, 2003
Szabados J; Erdélyi T: Bernstein inequalities for polynomials with constrained roots, Acta Sci. Math. (Szeged), 68: 163-178, 2002
Della Vecchia B; Mastroianni G; Vértesi P: One sided convergence condition of Lagrange interpolation based on generalized Jacobi type weights, Acta Math. Hugar. 99: 329-350, 2003
Szabados J; Gal SG: Partial shape preserving approximation by interpolation operators, In: Functions, Series, Operators, Alexits Memorial Conference (Budapest, 1999), 2002, pp. 225-246, 2002
Vértesi P: On the Lebesgue function and the Lebesgue constant, In: A tribute to Paul Erdős, Bolyai Society Math. Studies, 2002. pp. 705–728, 2002
Kroó, A; Szabados, J: On density of homogeneous polynomials on convex and star-like surfaces, East J. Approx., 11 (2005), 381-404, 2005
Szili L; Vértesi P: On uniform convergence of sequences of certain linear operators, Acta Math. Hungar. 91: 159–186, 2001
Brutman L; Gopengauz I; Vértesi P: On the domain of divergence of Hermite-Fejér interpolating polynomials, J. Appr. Theory 106: 287–289, 2000
Della Vecchia B; Mastroianni G; Vértesi P: Uniform convergence of Hermite-Fejér interpolation based on generalized Jacobi nodes, Rendiconti del Circolo Matematico di Palermo 68: 389–405, 2000
Vértesi P: On classical (unweighted) and weighted interpolation, Rendiconti del Circolo Matematico di Palermo 68: 185–202, 2000
Vértesi P: Problems in approximation theory (Hungarian), In: MTA Közgyűlési Előadások I, 2000. pp. 127–129, 2000
Gróf J: Uniform approximation on the whole real line, Department of Mathematics and Computing, University of Veszprém, Preprint No. 097, October 2002, 2002
Mastroianni G; Szabados J: Polynomial approximation on infinite intervals with weights having inner zeros, Acta Math. Hungar. 96: 221-258., 2002
Sharma A; Szabados J: A multivariate extension of Walsh\'s overconvergence theorem, Rendiconti del Circolo Matematico di Palermo, 68 (2002), 797-803., 2002
Kroó A; Szabados J: Tangential Bernstein--Markov inequalities for bivariate polynomials on curves, East J. Approx. 8: 261-278, 2002
Della Vecchia B; Mastroianni G; Szabados J: Approximation with exponential weights in [-1,1], J. Math. Anal. Appl. 272: 1-18, 2002
Erdélyi T; Szabados J: On a generalization of the Bernstein-Markov inequality, Algebra i Analiz, 14: 36-53, 2002
Szili L; Vértesi P: On summability of weighted Lagrange interpolation.II,, Acta Math. Hungar. 103: 1-17, 2004
Szili L; Vértesi P: On summability of weighted Lagrange interpolation.III, Acta Math. Hungar. 104: 39-62, 2004
Vértesi P: In memoriam Lev Brutman (1939 – 2001), J. of Approx. Th. 124: 1-6, 2003
Della Vecchia B; Mastroianni G; Szabados J: Weighted approximation of functions with inner singularities by iterated exponential weights, in [-1,1], Numer. Funct. Anal. and Optimiz., 24: 181-194., 2003
Della Vecchia B; Mastroianni G; Szabados J: Weighted approximation of functions with endpoint or inner singularities by iterated exponential weights, East J. Approx., 9: 214-227., 2003
Szabados J: Inequalities for polynomials with weights having infinitely many zeros ont he real line, In: Buhmann, Mache D.H. (ed.) Advanced problems in Constructive Approximation, ISNM Vol. 142, Birkhäuser, 2003. pp. 223-236, 2003
Vértesi P; Xu Y: Mean convergence of orthogonal Fourier series and interpolating polynomials, Acta Math. Hungar. 107: 125-154, 2005
Della Vecchia B; Mastroianni G; Szabados J: Weighted approximation of functions with endpoint or inner singularities by Bernstein operators, Acta Math. Hungar. 103: 19-41, 2004
Della Vecchia B; Mastroianni G; Szabados: Weighted approximation of functions on the real line by Bernstein polynomials, J. Approx. Theory, 127: 223-239, 2004
Vértesi, P.: Classical (unweighted) and Weighted Interpolation, A Panorama of Hungarian Mathematics in the Twentieth Century I., Bolyai Society Mathematical Studies, Vol.14, Springer, (2005), 71-117., 2005
Mastroianni, G.; Vértesi, P.: Fourier sums and Lagrange interpolation, Frontiers in Interpolation and Approximation (A. Sharma Memorial Volume) (megjelenés alatt), 2005
Szabados, J.: A strong converse result for approximation by weighted Bernstein polynomials on the real line, Trends and Application in Constructive Approximation (eds. M.G.de Bruin, D.H.Mache and J. Szabados), ISNM, Birkhauser Verlag, 247-258, 2005
Della Vecchia B; Mastroianni G; Vértesi P: Exact order of the Lebesgue constants for bivariate Lagrange interpolation at certain node-systems, Sudia Math. Hungar., 2007
Vértesi, P.: Results on Interpolation of Hungarian Mathematicians in the Twentieth Century, NUMERICAL ANALYSIS AND APPROXIMATION THEORY PROCEEDINGS OF THE INTERNATIONAL CONFERENCE ON NUMERICAL ANALYSIS AND APPROXIMATION THEORY NAAT 2006, CLUJ-NAPOCA, p. 1-18., 2006
Della Vecchia B; Mastroianni G; Szabados J: Weighted approximation of functions by Szász-Mirakyan-type operators, Acta Math. Hungar., 325-345., 2006
Szabados, J: Discrete linear interpolatory operators,, Surveys in Approximation Theory, 63-60., 2006
Mastroianni, G.; Szabados, J: Direct and converse polynomial approximation theorems on the real line with weights having zeros, Frontiers in Interpolation and Approximation (A. Sharma Memorial Volume), 287-306., 2006
Jakimovski, A.; Sharma, A; Szabados, J: Walsh Equiconvergence of Complex Interpolating Polynomials, Springer Math. Monograph Series, 2006



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