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Publications Influence

On differentiability and analyticity of positive definite functions

We derive a set of differential inequalities for positive definite functions based on previous results derived for positive definite kernels by purely algebraic methods. Our main results show that… Expand

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A linear algebraic approach to holomorphic reproducing kernels in Cn

Abstract Let Ω ⊆ C n be a domain and k be a holomorphic reproducing kernel on Ω . By the Moore–Aronszajn characterization, every finite matrix k ( Z i , Z j ) is positive semidefinite. We show that,… Expand

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Positive-Definiteness, Integral Equations and Fourier Transforms

- J. Buescu, A. Paixao, Francisco M. Garcia, I. Lourtie
- Mathematics
- 1 March 2004

We show that positive definite kernel functions k(x, y), if continuous and integrable along the main diagonal, coincide with kernels of positive integral operators in L2(R). Such an operator is shown… Expand

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Eigenvalue distribution of Mercer-like kernels

We study eigenvalues of positive definite kernels of L2 integral operators on arbitrary intervals. Assuming integrability and uniform continuity of the kernel on the diagonal, we show that the… Expand

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Positive definite matrices and differentiable reproducing kernel inequalities

Abstract Let I ⊆ R be a interval and k : I 2 → C be a reproducing kernel on I. By the Moore–Aronszajn theorem, every finite matrix k ( x i , x j ) is positive semidefinite. We show that, as a direct… Expand

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Positive-definiteness and integral representations for special functions

We characterize a holomorphic positive definite function $f$ defined on a horizontal strip of the complex plane as the Fourier-Laplace transform of a unique exponentially finite measure on… Expand

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Positive definite matrices and integral equations on unbounded domains

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A introdução da alienação fiduciária no direito brasileiro

- Ant'onio Paixao
- 2019

Propagation of regularity and positive definiteness: a constructive approach

- J. Buescu, A. Paixao, C. Oliveira
- Mathematics
- 8 January 2018

We show that, for positive definite kernels, if specific forms of regularity (continuity, Sn-differentiability or holomorphy) hold locally on the diagonal, then they must hold globally on the whole… Expand

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Real and complex variable positive definite functions

In this paper we present an overview of the implications of our previously derived results for positive definite kernels on the general theory of positive definite functions. We begin by exploring… Expand

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