Harmonic analysis, approximation theory and applications

• Grant number: 16/09906-0
• Support Opportunities: Research Projects - Thematic Grants
• Start date: December 01, 2016
• End date: November 30, 2021
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Dimitar Kolev Dimitrov
• Grantee: Dimitar Kolev Dimitrov
• Host 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
• Pesquisadores principais: Alagacone Sri Ranga ; Valdir Antonio Menegatto
• Associated researchers: Ana Paula Peron ; Cleonice Fátima Bracciali ; Thaís Jordão
• Associated research grant(s): 19/12413-4 - Topics in analysis and analytic number theory, AV.EXT; 17/02061-8 - Heine-Stieltjes theory and electrostatics, AV.EXT
• Associated scholarship(s): 21/13340-0 - Topic in classical analysis and approximation theory, BE.PQ; 18/00396-5 - Polynomials obtained from a recurrence relation which is a modification of the recurrence relation satisfied by orthogonal polynomials, BP.IC; 17/21605-9 - Orthogonal polynomials and differential equations, BP.IC; + associated scholarships 17/07442-0 - K-functionals of fractional orders and moduli of smoothness on a general setting, BE.PQ; 17/15223-6 - The Laguerre-Pólya class theory of functions and applications in the Analytic Number Theory, BP.PD; 17/04358-8 - Applications of functions satisfying certain recurrence relations, BP.DD - associated scholarships

Abstract

The principal objectives of this project are to study themes related to Harmonic Analysis, Approximation Theory and Special Functions and their Applications. Harmonic Analysis is a cornerstone of Analysis. The solutions of the principal partial differential equation are generally represented by convolutions and these representations are obtained via an application of the Fourier transform. Approximation Theory deals with fundamental questions as density of subspaces of a metric space and approximations of functions and functionals of a rather complex nature by simpler objects. The Theory of Special Functions is fundamental to describe quantitative properties of solutions of differential equations. The research in these areas and the connection between them facilitates the understanding of processes in nature and possesses various applications in other areas of Mathematics, and in Physics and Engineering. (AU)

Scientific publications

(33)

(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)

BISSIRI, PIER GIOVANNI; MENEGATTO, VALDIR A.; PORCU, EMILIO. Relations between Schoenberg Coefficients on Real and Complex Spheres of Different Dimensions. Symmetry Integrability and Geometry-Methods and Applications, v. 15, 2019. (16/09906-0)

BRACCIALI, CLEONICE F.; DA SILVA, V, JESSICA; RANGA, A. SRI. A class of Sobolev orthogonal polynomials on the unit circle and associated continuous dual Hahn polynomials: Bounds, asymptotics and zeros. Journal of Approximation Theory, v. 268, AUG 2021. (20/14244-2, 16/09906-0)

BRACCIALI, CLEONICE F.; PEREIRA, JUNIOR A.; RANGA, A. SRI. Quadrature rules from a R-II type recurrence relation and associated quadrature rules on the unit circle. NUMERICAL ALGORITHMS, v. 83, n. 3, p. 1029-1061, MAR 2020. (17/12324-6, 16/09906-0)

MARTINEZ-FINKELSHTEIN, A.; SILVA RIBEIR, L. L.; SRI RANGA, A.; TYAGLOV, M.. Complementary Romanovski-Routh Polynomials, Orthogonal Polynomials on the Unit Circle, and Extended Coulomb Wave Functions. Results in Mathematics, v. 75, n. 1, FEB 13 2020. (16/09906-0, 17/04358-8)

BRACCIALI, C. F.; MARTINEZ-FINKELSHTEIN, A.; SRI RANGA, A.; VERONESE, D. O.. Christoffel formula for kernel polynomials on the unit circle. Journal of Approximation Theory, v. 235, p. 46-73, NOV 2018. (17/12324-6, 16/09906-0)

BONFIM, RAFAELA N.; GUELLA, JEAN C.; MENEGATTO, VALDIR A.. Strictly Positive Definite Functions on Compact Two-Point Homogeneous Spaces: the Product Alternative. Symmetry Integrability and Geometry-Methods and Applications, v. 14, 2018. (16/09906-0, 14/14380-2)

OLIVEIRA, WILLIAN D.. Zeros of Dirichlet polynomials via a density criterion. JOURNAL OF NUMBER THEORY, v. 203, p. 80-94, OCT 2019. (13/14881-9, 17/15223-6, 16/09906-0)

DIMITROV, DIMITAR K.; XU, YUAN. WRONSKIANS OF FOURIER AND LAPLACE TRANSFORMS. TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, v. 372, n. 6, p. 4107-4125, SEP 15 2019. (16/09906-0, 14/08328-8)

CASTRO, MARIO H.; JORDAO, THAIS; PERON, ANA P.. Super-exponential decay rates for eigenvalues and singular values of integral operators on the sphere. Journal of Computational and Applied Mathematics, v. 364, JAN 15 2020. (16/09906-0, 16/02847-9, 17/07442-0)

DIMITROV, DIMITAR K.; SHAPIRO, BORIS. Electrostatic Problems with a Rational Constraint and Degenerate Lame Equations. POTENTIAL ANALYSIS, v. 52, n. 4, p. 645-659, APR 2020. (16/09906-0, 17/02061-8)

PERON, ANA; PORCU, EMILIO; EMERY, XAVIER. Admissible nested covariance models over spheres cross time. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, v. 32, n. 11, p. 3053-3066, NOV 2018. (16/03015-7, 16/09906-0)

CASTRO, MARIO H.; MASSA, EUGENIO; PERON, ANA PAULA. Characterization of Strict Positive Definiteness on products of complex spheres. POSITIVITY, v. 23, n. 4, p. 853-874, SEP 2019. (16/03015-7, 14/25796-5, 14/25398-0, 16/09906-0)

MARTINEZ-FINKELSHTEIN, A.; SILVA RIBEIRO, L. L.; SRI RANGA, A.; TYAGLOV, M.. COMPLEMENTARY ROMANOVSKI-ROUTH POLYNOMIALS: FROM ORTHOGONAL POLYNOMIALS ON THE UNIT CIRCLE TO COULOMB WAVE FUNCTIONS. Proceedings of the American Mathematical Society, v. 147, n. 6, p. 2625-2640, JUN 2019. (17/12324-6, 16/09906-0, 17/04358-8)

BERG, CHRISTIAN; PERON, ANA P.; PORCU, EMILIO. Schoenberg's theorem for real and complex Hilbert spheres revisited. Journal of Approximation Theory, v. 228, p. 58-78, APR 2018. (16/03015-7, 14/25796-5, 16/09906-0)

JORDAO, THAIS; MENEGATTO, VALDIR A.. Kolmogorov Widths on the Sphere via Eigenvalue Estimates for Holderian Integral Operators. Results in Mathematics, v. 74, n. 2, JUN 2019. (16/09906-0, 16/02847-9)

GUELLA, J. C.; MENEGATTO, V. A.. A LIMIT FORMULA FOR SEMIGROUPS DEFINED BY FOURIER-JACOBI SERIES. Proceedings of the American Mathematical Society, v. 146, n. 5, p. 2027-2038, MAY 2018. (16/09906-0)

BRACCIALI, CLEONICE F.; PEREZ, TERESA E.. Mixed orthogonality on the unit ball. COMPUTATIONAL & APPLIED MATHEMATICS, v. 40, n. 8, DEC 2021. (16/09906-0)

BORREGO-MORELL, JORGE A.; BRACCIALI, CLEONICE F.; RANGA, ALAGACONE SRI. On an Energy-Dependent Quantum System with Solutions in Terms of a Class of Hypergeometric Para-Orthogonal Polynomials on the Unit Circle. MATHEMATICS, v. 8, n. 7, JUL 2020. (16/09906-0)

RIBEIRO, LUANAL. SILVA; RANGA, A. SRI. A modified least squares method: Approximations on the unit circle and on (-1,1). Journal of Computational and Applied Mathematics, v. 410, p. 19-pg., 2022-08-15. (17/04358-8, 20/14244-2, 16/09906-0)

MENEGATTO, V. A.; OLIVEIRA, C. P.. Positive Definiteness on Products of Compact Two-point Homogeneous Spaces and Locally Compact Abelian Groups. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, v. 63, n. 4, p. 705-715, DEC 2020. (16/09906-0)

BRACCIALI, CLEONICE F.; SILVA, JAIRO S.; RANGA, A. SRI. Extended Relativistic Toda Lattice, L-Orthogonal Polynomials and Associated Lax Pair. ACTA APPLICANDAE MATHEMATICAE, v. 164, n. 1, p. 137-154, DEC 2019. (17/12324-6, 16/09906-0)

ISMAIL, M. E. H.; SRI RANGA, A.. R-II type recurrence, generalized eigenvalue problem and orthogonal polynomials on the unit circle. Linear Algebra and its Applications, v. 562, p. 63-90, FEB 1 2018. (17/12324-6, 16/09906-0)

DIMITROV, DIMITAR K.; OLIVEIRA, WILLIAN D.. Sign regularity of Maclaurin coefficients of functions in the Laguerre-Polya class. JOURNAL D ANALYSE MATHEMATIQUE, v. 137, n. 2, p. 897-911, MAR 2019. (13/14881-9, 16/09906-0)

GUELLA, J. C.; MENEGATTO, V. A.. Schoenberg's Theorem for Positive Definite Functions on Products: A Unifying Framework. JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS, v. 25, n. 4, p. 1424-1446, AUG 2019. (16/09906-0)

GUELLA, J. C.; MENEGATTO, V. A.. Unitarily invariant strictly positive definite kernels on spheres. POSITIVITY, v. 22, n. 1, p. 91-103, MAR 2018. (16/09906-0)

DIMITROV, DIMITAR K.; PEIXOTO, LOURENCO L.. AN EFFICIENT ALGORITHM FOR THE CLASSICAL LEAST SQUARES APPROXIMATION. SIAM JOURNAL ON SCIENTIFIC COMPUTING, v. 42, n. 5, p. A3233-A3249, 2020. (16/09906-0)

BISSIRI, PIER GIOVANNI; PERON, ANA PAULA; PORCU, EMILIO. Strict positive definiteness under axial symmetry on the sphere. STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT, v. 34, n. 5, MAY 2020. (16/09906-0)

MARCELLAN, F.; RANGA, A. SRI. Sobolev Orthogonal Polynomials on the Unit Circle and Coherent Pairs of Measures of the Second Kind. Results in Mathematics, v. 71, n. 3-4, p. 1127-1149, JUN 2017. (16/09906-0)

GUELLA, JEAN CARLO; MENEGATTO, VALDIR ANTONIO; PORCU, EMILIO. Strictly positive definite multivariate covariance functions on spheres. JOURNAL OF MULTIVARIATE ANALYSIS, v. 166, p. 150-159, JUL 2018. (16/09906-0)

GUELLA, J. C.; MENEGATTO, V. A.. Positive definite matrix functions on spheres defined by hypergeometric functions. INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, v. 30, n. 10, MAY 2019. (16/09906-0)

DIMITROV, DIMITAR K.; NIKOLOV, GENO P.. A discrete weighted Markov-Bernstein inequality for sequences and polynomials. Journal of Mathematical Analysis and Applications, v. 493, n. 1, JAN 1 2021. (16/10357-1, 16/09906-0)

MARCATO, GUSTAVO; RANGA, A. SRI; LUN, YEN CHI. PARAMETERS OF A POSITIVE CHAIN SEQUENCE ASSOCIATED WITH ORTHOGONAL POLYNOMIALS. Proceedings of the American Mathematical Society, v. 150, n. 6, p. 15-pg., 2022-06-01. (20/14244-2, 16/09906-0)

DIMITROV, DIMITAR K.; GADJEV, IVAN; NIKOLOV, GENO; ULUCHEV, RUMEN. HARDY'S INEQUALITIES IN FINITE DIMENSIONAL HILBERT SPACES. Proceedings of the American Mathematical Society, v. 149, n. 6, p. 15-pg., 2021-06-01. (16/10357-1, 16/09906-0)