Analysis of integral operators generated by positive definite kernels

• Grant number: 10/19734-6
• Support type: Regular Research Grants
• Duration: March 01, 2011 - February 28, 2013
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal researcher: Valdir Antonio Menegatto
• Grantee: Valdir Antonio Menegatto
• Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Integral operators are animportant tool in the formulation of several problems within pureand applied mathematics, for example, those in approximation theory,operator theory, classical analysis, learning theory, etc.\ Thisproject intends to consider some problems involving such operators,namely some related to Mercer's theory, reproducing kernel Hilbertspaces and eigenvalue decay, all aligned with recent research beingdeveloped by the proposer and its research group. (AU)

Scientific publications

(12)

(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)

CASTRO, M. H.; MENEGATTO, V. A.; PERON, A. P.. INTEGRAL OPERATORS GENERATED BY MERCER-LIKE KERNELS ON TOPOLOGICAL SPACES. Colloquium Mathematicum, v. 126, n. 1, p. 125-138, 2012. (10/19734-6)

FERREIRA, J. C.; MENEGATTO, V. A.. Reproducing kernel Hilbert spaces associated with kernels on topological spaces. Functional Analysis and its Applications, v. 46, n. 2, p. 152-154, APR 2012. (10/19734-6)

CASTRO, M. H.; MENEGATTO, V. A.. EIGENVALUE DECAY OF POSITIVE INTEGRAL OPERATORS ON THE SPHERE. Mathematics of Computation, v. 81, n. 280, p. 2303-2317, OCT 2012. (10/19734-6)

AZEVEDO, D.; MENEGATTO, V. A.. EIGENVALUE DECAY OF INTEGRAL OPERATORS GENERATED BY POWER SERIES-LIKE KERNELS. Mathematical Inequalities & Applications, v. 17, n. 2, p. 693-705, APR 2014. (10/19734-6, 10/00478-0)

MENEGATTO, V. A.; OLIVEIRA, C. P.. An Extension of Mercer's Theorem via Pontryagin Spaces. Integral Equations and Operator Theory, v. 74, n. 3, p. 363-375, NOV 2012. (10/19734-6)

DE CASTRO, MARIO H.; MENEGATTO, VALDIR A.; PERON, ANA P.. TRACEABILITY OF POSITIVE INTEGRAL OPERATORS IN THE ABSENCE OF A METRIC. Banach Journal of Mathematical Analysis, v. 6, n. 2, p. 98-112, 2012. (10/19734-6)

CASTRO, M. H.; MENEGATTO, V. A.; OLIVEIRA, C. P.. Laplace-Beltrami differentiability of positive definite kernels on the sphere. Acta Mathematica Sinica - English Series, v. 29, n. 1, p. 93-104, JAN 2013. (10/19734-6)

MENEGATTO, V. A.; OLIVEIRA, C. P.. Eigenvalue and singular value estimates for integral operators: a unifying approach. Mathematische Nachrichten, v. 285, n. 17-18, p. 2222-2232, DEC 2012. (10/19734-6)

FERREIRA, J. C.; MENEGATTO, V. A.. Eigenvalue decay rates for positive integral operators. Annali di Matematica Pura ed Applicata, v. 192, n. 6, p. 1025-1041, DEC 2013. (10/19734-6)

JORDAO, T.; MENEGATTO, V. A.. Weighted Fourier-Laplace transforms in reproducing kernel Hilbert spaces on the sphere. Journal of Mathematical Analysis and Applications, v. 411, n. 2, p. 732-741, MAR 15 2014. (10/19734-6)

AZEVEDO, D.; MENEGATTO, V. A.. Sharp estimates for eigenvalues of integral operators generated by dot product kernels on the sphere. Journal of Approximation Theory, v. 177, p. 57-68, JAN 2014. (10/19734-6, 10/00478-0)

FERREIRA, J. C.; MENEGATTO, V. A.. POSITIVE DEFINITENESS, REPRODUCING KERNEL HILBERT SPACES AND BEYOND. ANNALS OF FUNCTIONAL ANALYSIS, v. 4, n. 1, p. 64-88, 2013. (10/19734-6)