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Orthogonal polynomials, special functions and applications

Grant number: 09/13832-9
Support type:Research Projects - Thematic Grants
Duration: July 01, 2010 - June 30, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics
Principal Investigator:Dimitar Kolev Dimitrov
Grantee:Dimitar Kolev Dimitrov
Home Institution: Instituto de Biociências, Letras e Ciências Exatas (IBILCE). Universidade Estadual Paulista (UNESP). Campus de São José do Rio Preto. São José do Rio Preto , SP, Brazil
Co-Principal Investigators:Alagacone Sri Ranga
Assoc. researchers:Cleonice Fátima Bracciali ; Eliana Xavier Linhares de Andrade
Associated grant(s):15/01545-6 - Topics in Fourier analysis and number theory, AV.EXT
14/17357-1 - Orthogonal polynomials and fast multipole method, AV.EXT
14/08328-8 - Harmonic analysis and multivariate orthogonal polynomials, AV.EXT
13/23606-1 - Methods for approximate calculus of sums and series, AV.EXT
13/15840-4 - Optimal recovery and Extremum problems: methods and solutions, AV.EXT
Associated scholarship(s):13/19551-7 - Orthogonal polynomials on the real line and on the unit circle, BP.PD
13/14881-9 - Harmonic analysis and Number Theory, BP.DR
13/11896-5 - Orthogonal polynomials and related topics, BP.IC
+ associated scholarships 12/21042-0 - Orthogonal polynomials with respect to differential operators and matrix orthogonal polynomials, BP.PD
12/11228-0 - Ortogonal polynomials on the real line and on the unit circle, BP.IC
10/13543-4 - Orthogonal polynomials and random matrices: study and characterization via Riemann-Hilbert problem, BP.MS - associated scholarships

Abstract

The scientific aim of this project is the study of the general properties of the orthogonal polynomials, special functions and their applications to both Applied Mathematics and various areas of Pure Mathematics. This is the principal theme of the studies of our research group. These polynomials and functions have important applications to various areas of Classical Analysis and Numerical Analysis: Numerical Quadrature Formulae; Least Square Approximations, including Fourier series; Padé Approximations and the Theory of Continued Fractions; Approximations by splines; Moment Preserving Approximations; Relaxation Methods in Linear Algebra; Polynomial Inequalities and Polynomial Regression and "birth and death" processes in Statistics. While the majority of these topics can be considered to belong to Applied Mathematics, other applications to Code Theory; Potential Theory; Zeros of Polynomials and Functions are related to Algebra, Differential Equations, Complex Analysis and Classical Real Analysis. Some of the remarkable applications and connections of the orthogonal polynomials are the use of certain inequalities for sums of Jacobi polynomials in de Branges' proof of 1984 of the Bieberbach conjecture about the coefficients of univalent functions, formulated in 1916, as well as the tight relation between the distribution of the zeros of the Riemann zeta function and the eigenvalues of certain random matrices, described by the Law of Montgomery e Dyson, from one side, and these matrices and orthogonal polynomials, from the other. The members of the research group Alagacone Sri Ranga, Cleonice Fátima Bracciali, Dimitar Kolev Dimitrov and Eliana Xavier Linhares de Andrade have contributed to the theory and applications of orthogonal polynomials and special functions with more than 100 high quality research papers and supervised tens of PhD and Master students. Some of our students already do independent research; others have won national and international prizes and awards. The group has been supported by important research projects of the foundations FAPESP, CNPq and CAPES, both of national level and by international exchange programs. The purpose of the group is to continue contributing in research through new publications and transmitting the acquired knowledge to talented students in order to form a new generation of good Brazilian mathematicians. (AU)

Scientific publications (20)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
MARTINEZ-FINKELSHTEIN, A.; RANGA, A. SRI; VERONESE, D. O. EXTREME ZEROS IN A SEQUENCE OF PARA-ORTHOGONAL POLYNOMIALS AND BOUNDS FOR THE SUPPORT OF THE MEASURE. Mathematics of Computation, v. 87, n. 309, p. 261-288, JAN 2018. Web of Science Citations: 3.
BRACCIALI, C. F.; RANGA, A. SRI; SWAMINATHAN, A. Para-orthogonal polynomials on the unit circle satisfying three term recurrence formulas. APPLIED NUMERICAL MATHEMATICS, v. 109, p. 19-40, NOV 2016. Web of Science Citations: 6.
BARICZ, ARPAD; DIMITROV, DIMITAR K.; ORHAN, HALIT; YAGMUR, NIHAT. RADII OF STARLIKENESS OF SOME SPECIAL FUNCTIONS. Proceedings of the American Mathematical Society, v. 144, n. 8, p. 3355-3367, AUG 2016. Web of Science Citations: 15.
BRACCIALI, C. F.; MCCABE, J. H.; PEREZ, T. E.; RANGA, A. SRI. A CLASS OF ORTHOGONAL FUNCTIONS GIVEN BY A THREE TERM RECURRENCE FORMULA. Mathematics of Computation, v. 85, n. 300, p. 1837-1859, JUL 2016. Web of Science Citations: 6.
DIMITROV, DIMITAR K.; XU, YUAN. Slater determinants of orthogonal polynomials. Journal of Mathematical Analysis and Applications, v. 435, n. 2, p. 1552-1572, MAR 15 2016. Web of Science Citations: 1.
BARICZ, ARPAD; DIMITROV, DIMITAR K.; MEZO, ISTVAN. Radii of starlikeness and convexity of some q-Bessel functions. Journal of Mathematical Analysis and Applications, v. 435, n. 1, p. 968-985, MAR 1 2016. Web of Science Citations: 10.
RANGA, A. SRI. ORTHOGONAL POLYNOMIALS WITH RESPECT TO A FAMILY OF SOBOLEV INNER PRODUCTS ON THE UNIT CIRCLE. Proceedings of the American Mathematical Society, v. 144, n. 3, p. 1129-1143, MAR 2016. Web of Science Citations: 1.
DIMITROV, DIMITAR K.; DOS SANTOS, ELIEL J. C. ASYMPTOTIC BEHAVIOUR OF JACOBI POLYNOMIALS AND THEIR ZEROS. Proceedings of the American Mathematical Society, v. 144, n. 2, p. 535-545, FEB 2016. Web of Science Citations: 1.
BORREGO-MORELL, J.; RANGA, A. SRI. Orthogonal polynomials on the unit circle satisfying a second-order differential equation with varying polynomial coefficients. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, v. 28, n. 1, p. 39-55, JAN 2016. Web of Science Citations: 0.
AREA, IVAN; DIMITROV, DIMITAR K.; GODOY, EDUARDO; PASCHOA, VANESSA G. APPROXIMATE CALCULATION OF SUMS II: GAUSSIAN TYPE QUADRATURE. SIAM JOURNAL ON NUMERICAL ANALYSIS, v. 54, n. 4, p. 2210-2227, 2016. Web of Science Citations: 2.
BEHERA, KIRAN KUMAR; SRI RANGA, A.; SWAMINATHAN, A. Orthogonal Polynomials Associated with Complementary Chain Sequences. Symmetry Integrability and Geometry-Methods and Applications, v. 12, 2016. Web of Science Citations: 0.
BRACCIALI, CLEONICE F.; SILVA, JAIRO S.; RANGA, A. SRI. Explicit formulas for OPUC and POPUC associated with measures which are simple modifications of the Lebesgue measure. Applied Mathematics and Computation, v. 271, p. 820-831, NOV 15 2015. Web of Science Citations: 3.
AREA, IVAN; DIMITROV, DIMITAR K.; GODOY, EDUARDO; PASCHOA, VANESSA. Bounds for the zeros of symmetric Kravchuk polynomials. NUMERICAL ALGORITHMS, v. 69, n. 3, p. 611-624, JUL 2015. Web of Science Citations: 1.
COSTA, M. S.; LAMBLEM, R. L.; MCCABE, J. H.; RANGA, A. SRI. Para-orthogonal polynomials from constant Verblunsky coefficients. Journal of Mathematical Analysis and Applications, v. 426, n. 2, p. 1040-1060, JUN 15 2015. Web of Science Citations: 2.
AREA, IVAN; DIMITROV, DIMITAR K.; GODOY, EDUARDO. Zero sets of bivariate Hermite polynomials. Journal of Mathematical Analysis and Applications, v. 421, n. 1, p. 830-841, JAN 1 2015. Web of Science Citations: 2.
DIMITROV, DIMITAR K.; LUN, YEN CHI. Monotonicity, interlacing and electrostatic interpretation of zeros of exceptional Jacobi polynomials. Journal of Approximation Theory, v. 181, p. 18-29, MAY 2014. Web of Science Citations: 6.
AREA, IVAN; DIMITROV, DIMITAR K.; GODOY, EDUARDO; PASCHOA, VANESSA. APPROXIMATE CALCULATION OF SUMS I: BOUNDS FOR THE ZEROS OF GRAM POLYNOMIALS. SIAM JOURNAL ON NUMERICAL ANALYSIS, v. 52, n. 4, p. 1867-1886, 2014. Web of Science Citations: 6.
DIMITROV, DIMITAR K.; ISMAIL, MOURAD E. H.; RAFAELI, FERNANDO R. Interlacing of zeros of orthogonal polynomials under modification of the measure. Journal of Approximation Theory, v. 175, p. 64-76, NOV 2013. Web of Science Citations: 3.
CASTILLO, K.; DIMITROV, D. K.; GARZA, L. E.; RAFAELI, F. R. Perturbations on the antidiagonals of Hankel matrices. Applied Mathematics and Computation, v. 221, p. 444-452, SEP 15 2013. Web of Science Citations: 4.
AREA, IVAN; DIMITROV, DIMITAR K.; GODOY, EDUARDO; PASCHOA, VANESSA G. ZEROS OF CLASSICAL ORTHOGONAL POLYNOMIALS OF A DISCRETE VARIABLE. Mathematics of Computation, v. 82, n. 282, p. 1069-1095, APR 2013. Web of Science Citations: 5.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.