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Harmonic analysis, approximation theory and applications

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)

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Scientific publications (30)
(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)
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, . (13/14881-9, 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, . (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, . (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, . (17/12324-6, 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, . (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, . (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, . (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, . (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, . (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, . (17/12324-6, 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, . (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, . (16/10357-1, 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, . (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, . (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, . (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, . (16/09906-0, 16/02847-9, 17/07442-0)
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, . (17/12324-6, 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, . (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, . (16/09906-0, 14/14380-2)
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, . (16/03015-7, 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, . (20/14244-2, 16/09906-0)
OLIVEIRA, WILLIAN D.. Zeros of Dirichlet polynomials via a density criterion. JOURNAL OF NUMBER THEORY, v. 203, p. 80-94, . (13/14881-9, 16/09906-0, 17/15223-6)
DIMITROV, DIMITAR K.; SHAPIRO, BORIS. Electrostatic Problems with a Rational Constraint and Degenerate Lame Equations. POTENTIAL ANALYSIS, v. 52, n. 4, p. 645-659, . (16/09906-0, 17/02061-8)
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, . (16/03015-7, 14/25796-5, 14/25398-0, 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, . (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, . (16/09906-0, 17/04358-8)
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, . (16/09906-0)
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, . (16/03015-7, 14/25796-5, 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, . (16/09906-0)
BRACCIALI, CLEONICE F.; PEREZ, TERESA E.. Mixed orthogonality on the unit ball. COMPUTATIONAL & APPLIED MATHEMATICS, v. 40, n. 8, . (16/09906-0)

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