New characterizations of reproducing kernel Hilbert spaces and applications to metric geometry [PDF]
Opuscula Mathematica, 2021 We give two new global and algorithmic constructions of the reproducing kernel Hilbert space associated to a positive definite kernel. We further present a general positive definite kernel setting using bilinear forms, and we provide new examples.
Daniel Alpay, Palle E.T. Jorgensen
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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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A Discussion on the Existence of Smooth Lyapunov Functions for Continuous Stable Systems [PDF]
International Journal of Industrial Electronics, Control and Optimization, 2021 Lyapunov's theorem is the basic criteria to establish the stability properties of the nonlinear dynamical systems. In this method, it is a necessity to find the positive definite functions with negative definite or negative semi-definite derivative ...
Majid Akbarian, Naser Pariz
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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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Positive definite functions and dual pairs of locally convex spaces [PDF]
Opuscula Mathematica, 2018 Using pairs of locally convex topological vector spaces in duality and topologies defined by directed families of sets bounded with respect to the duality, we prove general factorization theorems and general dilation theorems for operator-valued positive
Daniel Alpay, Saak Gabriyelyan
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Evenly positive definite function of Hilbert space and some algebraic relationship
Математичні Студії, 2021 A generalization of P. A. Minlos, V. V. Sazonov’s theorem is proved in the case of bounded evenly positive definite function given in a Hilbert space.
O. V. Lopotko
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Non-Debye Relaxations: Two Types of Memories and Their Stieltjes Character
Mathematics, 2021 In this paper, we show that spectral functions relevant for commonly used models of the non-Debye relaxation are related to the Stieltjes functions supported on the positive semi-axis.
Katarzyna Górska, Andrzej Horzela
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POSITIVE DEFINITE FUNCTIONS AND SHARP INEQUALITIES FOR PERIODIC FUNCTIONS
Ural Mathematical Journal, 2017 Let \(\varphi\) be a positive definite and continuous function on \(\mathbb{R}\), and let \(\mu\) be the corresponding Bochner measure. For fixed \(\varepsilon,\tau\in\mathbb{R}\), \(\varepsilon\ne 0\), we consider a linear operator \(A_{\varepsilon,\tau}
Viktor P. Zastavnyi
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On Matrix-Valued Square Integrable Positive Definite Functions [PDF]
, 2015 In this paper, we study matrix valued positive definite functions on a unimodular group. We generalize two important results of Godement on square integrable positive definite functions to matrix valued square integrable positive definite functions.
He, Hongyu
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Stability of solutions and the problem of Aizerman for sixth-order differential equations
Журнал Белорусского государственного университета: Математика, информатика, 2020 This article is devoted to the investigation of stability of equilibrium of ordinary differential equations using the method of semi-definite Lyapunov’s functions.
Boris S. Kalitine
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