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Strictly Hermitian Positive Definite Functions
, 2004 Let H be any complex inner product space with inner product . We say that f : C -->C is Hermitian positive definite on H if the matrix $$(f())_{r,s=1}^n \eqno(*)$$ is Hermitian positive definite for all choice of z^1,...,z^n in H, all n.
Pinkus, Allan
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A Note on the Derivatives of Isotropic Positive Definite Functions on the Hilbert Sphere [PDF]
, 2019 In this note we give a recursive formula for the derivatives of isotropic positive definite functions on the Hilbert sphere. We then use it to prove a conjecture stated by Tr\"ubner and Ziegel, which says that for a positive definite function on the ...
Jäger, Janin
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Positive definite functions and Karhunen-Loeve Theorem [PDF]
, 2015 Εθνικό Μετσόβιο Πολυτεχνείο--Μεταπτυχιακή Εργασία. Διεπιστημονικό-Διατμηματικό Πρόγραμμα Μεταπτυχιακών Σπουδών (Δ.Π.Μ.Σ.) “Μαθηματική Προτυποποίηση σε Σύγχρονες Τεχνολογίες στην ...
Katsimardou, Sofia +1 more
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Strictly positive definite functions on compact abelian groups
, 2010 We study the Fourier characterisation of strictly positive definite functions on compact abelian groups. Our main result settles the case $G = F \times \mathbb{T}^r$, with $r \in \mathbb{N}$ and $F$ finite.
Emonds, Jan, Fuehr, Hartmut
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Evaluating functions of positive-definite matrices using colored noise thermostats [PDF]
, 2014 Many applications in computational science require computing the elements of a function of a large matrix. A commonly used approach is based on the the evaluation of the eigenvalue decomposition, a task that, in general, involves a computing time that ...
Ceriotti, Michele +3 more
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Positive Definite Norm Dependent Matrices In Stochastic Modeling
Demonstratio Mathematica, 2014 Positive definite norm dependent matrices are of interest in stochastic modeling of distance/norm dependent phenomena in nature. An example is the application of geostatistics in geographic information systems or mathematical analysis of varied spatial ...
Kuniewski Sebastian P. +1 more
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Advances in Mathematical Physics, 2022 In this paper, we consider semidiscrete splitting positive definite mixed finite element methods for optimal control problems governed by hyperbolic equations with integral constraints.
Yuchun Hua, Yuelong Tang
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Reproducing Kernel Hilbert Spaces of Smooth Fractal Interpolation Functions
Fractal and Fractional, 2023 The theory of reproducing kernel Hilbert spaces (RKHSs) has been developed into a powerful tool in mathematics and has lots of applications in many fields, especially in kernel machine learning.
Dah-Chin Luor, Liang-Yu Hsieh
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Vertex corrections for positive-definite spectral functions of simple metals [PDF]
, 2016 We present a systematic study of vertex corrections in the homogeneous electron gas at metallic densities. The vertex diagrams are built using a recently proposed positive-definite diagrammatic expansion for the spectral function. The vertex function not
Pavlyukh, Y. +3 more
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Intrinsic data depth for Hermitian positive definite matrices
, 2018 Nondegenerate covariance, correlation and spectral density matrices are necessarily symmetric or Hermitian and positive definite. The main contribution of this paper is the development of statistical data depths for collections of Hermitian positive ...
Chau, Joris +2 more
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