Journal of Advances in Applied Mathematics
A Study of Weighted Polynomial Approximations for Orthogonal Polynomial Expansion
- Ryozi Sakai*
Department of Mathematics, Meijo University, Tenpaku-ku, Nagoya 468-8502, Japan
 S. B. Damelin and D. S. Lubinsky, Jackson Theorems for Erd¨os Weights in Lp (0 < p≤ ∞), Journal of Approximation Theory 94(1998), 333-382.
 H. S. Jung and R. Sakai, Higher order derivatives of approximation polynomial on R, Journal of inequalities and applications, 2015: 268, DOI 10.1186/s13660-o15-0789-y.
 D. S. Lubinsky, A Survey of Weighted Polynomial Approximation with Exponential Weights, Surveys on Approximation Theory, 3(2007), 1-105.
 A. L. Levin and D. S. Lubinsky, Orthogonal Polynomials for Exponential Weights, Springer, New York, 2001.
 H. N. Mhaskar, Extensions of the Dirichlet?Jordan Convergence Criterion to a General Class of Orthogonal Polynomial Expansions, Journal of Approximation Theory 42 (1984), 138-148.
 W. Rudin, Principles of Mathematical Analysis, McGraw-Hill, New York, 1964.
 R. Sakai and N. Suzuki, Favard-type inequalities for exponential weights, Pioneer J. of Math. vol 3. No.1, 2011, 1-16.
 R. Sakai and N. Suzuki, Mollification of exponential weights and its application to the Markov-Bernstein inequality, Pioneer J. of Math., Vol.7, no.1, pp.83-101, 2013.
 K. Itoh, R. Sakai and N. Suzuki, The de la Vall′ee Poussin Mean and Polynomial Appoximation for Exponential Weight, International Journal of Analysis, 2015, Article ID 706930, 8 pages, (2015).
 K. Itoh, R. Sakai and N. Suzuki, An estimate for derivative of the de la Vall′ee Poussin mean, Math. J. Ibaraki Univ. 47 (2015), 1-18.
 K. Itoh, R. Sakai and N. Suzuki, Uniform convergence of orthogonal polynomial expansions for exponential weights, preprint.
 K. Itoh, R. Sakai and N. Suzuki, Polynomial approximation for absolutely continuous functions, accepted by Tohoku Math. Journal.