Results 11 to 20 of about 7,594,968 (240)
Approximation by Positive Definite Functions on Compact Groups
Numerical Functional Analysis and Optimization, 2008 We consider approximation methods defined by translates of a positive definite function on a compact group. A characterization of the native space generated by a positive definite function on a compact group is presented.
Wolfgang Erb, Frank Filbir
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Derivatives of isotropic positive definite functions on spheres [PDF]
, 2017 We show that isotropic positive definite functions on the d -dimensional sphere which are 2k times differentiable at zero have 2k+[(d−1)/2] continuous derivatives on (0,π) .
Trübner, Mara, Ziegel, Johanna F.
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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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Convolution roots and differentiability of isotropic positive definite functions on spheres [PDF]
, 2014 We prove that any isotropic positive definite function on the sphere can be written as the spherical self-convolution of an isotropic real-valued function.
Ziegel, Johanna F.
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Positive definite functions on a regular domain [PDF]
, 2023 We define positive and strictly positive definite functions on a domain and study these functions on a list of regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid, and simplex.
Xu, Yuan, Buhmann, Martin
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Continuations of Hermitian indefinite functions and corresponding canonical systems : an example [PDF]
, 2004 M. G. Krein established a close connection between the continuation problem of positive definite functions from a finite interval to the real axis and the inverse spectral problem for differential operators.
Sasvári, Zoltán +2 more
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Functional Calculus and Positive-Definite Functions [PDF]
Transactions of the American Mathematical Society, 1977 For a LCA group G with dual group Ĝ , let D ( G
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On Positive Definiteness of Some Functions
Journal of Multivariate Analysis, 2000 Let \(E\) be a linear space over \(\mathbb{R}\) and let \(\rho(x)\) be the \(\ell^n_p\)-norm in \(\mathbb{R}^n\). A function \(f: E\to\mathbb{C}\) is called definite if \(\sum^n_{k,j=1} c_k\overline c_jf(x_k- x_j)\geq 0\) for all \(n\in\mathbb{N}\), \(x_k\in E\), \(c_k\in\mathbb{C}\) for \(k= 1,2,\dots, n\).
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Isotropic positive definite functions on spheres
Journal of Functional Analysis, 2022 In this paper, we investigate the relationship between positive definite functions on the unit sphere $\sph$ and on the Euclidean space $\RR^d$. For the dimension $d$ to be odd, a new technique is developed to establish the inheritance of positive (semi-)definite property from $\RR^d$ to $\sph$ and the converse.
Han Feng, Yan Ge
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Relationship Between Neurologic Symptoms and Signs and FMR1 Genotype in Premutation Carriers
Annals of Clinical and Translational Neurology, EarlyView.ABSTRACT Background and Objectives Fragile X‐associated Tremor/Ataxia Syndrome (FXTAS) is the most severe late‐onset condition caused by a premutation in the FMR1 gene, characterized by expanded CGG triplet repeats of 55–200. Clinical presentations of FXTAS, including gait ataxia, kinetic tremor, cognitive decline, and rare Parkinsonism, are linked to ...
Flora Tassone +8 more
wiley +1 more source