Theory of Polynomials and Applications : Recent Advances

Contents Preface. 1. Some generalizations of Enestrom Kakeya Theorem/Atif Abueida and Robert Gardner. 2. Information technology the life groups defining the filter banks of the compact disc/Ernst Binz and Walter Schempp. 3. On the distribution of alteration points in uniform rational approximation/H.P. Blatt R. Grothmann and R.K. Kovacheva. 4. (N+1) dimensional Nonlinear Schrodinger equation and its Soliton solutions/A.V. Borzykh. 5. LP Inequalities for polynomials with restricted zeros/K.K. Dewan Harish Singh and R.S. Yadav. 6. Converse of an extremal problem in polynomials/B. Datt and Indu Kaushik. 7. The relative errors of the approximations of Chebyshev polynomial zeros/Masao Igarashi and Eiji Nunohiro. 8. Direct estimates of maximum modulus maximum term and interpolation error of an entire function/Devendra Kumar. 9. Bernstein type inequalities for the polar derivatives of a polynomial/N.K. Govil and G.N. McTume. 10. On the approximation by reciprocals of polynomials with positive coefficients in L1 space/X.F. Mei and S.P. Zhou. 11. An extremal problem for Algebraic polynomials with a prescribed zero/Igor Z. Milovanovic. 12. Harmonic polynomials and generalizations of Ostrowski inequality and Taylor formula/J. Pecaric and A. Vukelic. 13. Remarks on the order of approximation of Hermite and Hermite Fejer interpolation of Jacobi Abscissas of Pn(a a)(x)/J. Prasad and Jhunjhunwala. 14. Cauchy polynomials/G. Schmeisser. 15. Distributions involving Meijer's G function of Matrix argument in complex case/P.L. Sethi and M.B. El Khazendar. 16. Two sided inequalities involving certain families of orthogonal polynomials and special functions/H.M. Srivastava. 17. On the zeros of a polynomial/C.M. Upadhye. 18. Turan type inequalities/J.L. Wang and S.P. Zhou. 19. Inequalities for a derivative of a polynomial/R.S. Yadav K.K. Dewan and Harish Singh. 20. Some refinements of Enestrom Kakeya Theorem/B.A. Zargar and Abdul Aziz. Index. This truly outstanding work is a collection of 20 selected papers by 31 internationally distinguished mathematicians investigating the open problems in Theory of Polynomials and its Applications. The articles discuss recent advances problems and their current status as well as historical background of the subject such as Bernstein and Markov type of inequalities Turan type inequalities Lp inequalities for polynomials extremal problems of Algebraic polynomials approximations by reciprocals of polynomials with positive co efficients in L1 space relative errors of the approximations of Chebyshev polynomial zeros harmonic polynomials Cauchy polynomials orthogonal polynomials Enestrom Kakeya Theorem and interpolation errors of an entire function. 228 pp.…