Results 1 to 10 of about 2,773 (119)
A Note on n-Divisible Positive Definite Functions
Journal of Mathematics, 2022 Let PDℝ be the family of continuous positive definite functions on ℝ. For an integer n>1, a f∈PDℝ is called n-divisible if there is g∈PDℝ such that gn=f. Some properties of infinite-divisible and n-divisible functions may differ in essence.
Saulius Norvidas
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On functional reproducing kernels
Open Mathematics, 2023 We show that even if a Hilbert space does not admit a reproducing kernel, there could still be a kernel function that realizes the Riesz representation map.
Zhou Weiqi
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mbend: an R package for bending non-positive-definite symmetric matrices to positive-definite
BMC Genetics, 2020 Background R package mbend was developed for bending symmetric non-positive-definite matrices to positive-definite (PD). Bending is a procedure of transforming non-PD matrices to PD.
Mohammad Ali Nilforooshan
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Positive Inductive-Recursive Definitions [PDF]
Logical Methods in Computer Science, 2013 A new theory of data types which allows for the definition of types as initial algebras of certain functors Fam(C) -> Fam(C) is presented. This theory, which we call positive inductive-recursive definitions, is a generalisation of Dybjer and Setzer's theory of inductive-recursive definitions within which C had to be discrete -- our work can ...
Ghani, Neil +2 more
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Journal of Inequalities and Applications, 2016 We consider two nonlinear matrix equations X r ± ∑ i = 1 m A i ∗ X δ i A i = I $X^{r} \pm \sum_{i = 1}^{m} A_{i}^{*}X^{\delta_{i}}A_{i} = I$ , where − 1 < δ i < 0 $- 1 < \delta_{i} < 0$ , and r, m are positive integers. For the first equation (plus case),
Abdel-Shakoor M Sarhan +1 more
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Continuation of Radial Positive Definite Functions and Their Characterization
Fractal and Fractional, 2023 This paper delves into the extension and characterization of radial positive definite functions into non-integer dimensions. We provide a thorough investigation by employing the Riemann–Liouville fractional integral and fractional Caputo derivatives ...
Fethi Bouzeffour
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On the Positive Definiteness of a Functional [PDF]
Canadian Mathematical Bulletin, 1979 AbstractIn this note, we have shown that the set of conditions given by Gel'fand and Vilenkin for the positive definiteness of a functional L(ϕ) [1, Theorem 7, p. 285] though sufficient is not necessary, thereby providing an answer to an open problem posed by them [1, Theorem 7, p. 285].
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Two new eigenvalue localization sets for tensors and theirs applications
Open Mathematics, 2017 A new eigenvalue localization set for tensors is given and proved to be tighter than those presented by Qi (J. Symbolic Comput., 2005, 40, 1302-1324) and Li et al. (Numer. Linear Algebra Appl., 2014, 21, 39-50).
Zhao Jianxing, Sang Caili
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有关矩阵广义逆的惯性指数及其应用(Inertia formulae related to the generalized inverse with applications)
Zhejiang Daxue xuebao. Lixue ban, 2019 In this paper, firstly, we establish the inertia formulae for some matrix expressions related to the generalized inverse . Then, as applications, based on the derived inertia formulae, we study the definiteness of some matrices.
WUZhongcheng(吴中成) +1 more
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Convex maps on $\protect \mathbb{R}^n$ and positive definite matrices
Comptes Rendus. Mathématique, 2020 We obtain several convexity statements involving positive definite matrices. In particular, if $A,B,X,Y$ are invertible matrices and $A,B$ are positive, we show that the map \[ (s,t) \mapsto \mathrm{Tr}\,\log \left(X^*A^sX + Y^*B^tY\right) \] is jointly ...
Bourin, Jean-Christophe, Shao, Jingjing
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