Abstract
We consider the class of radial exponentially convex functions defined over n-dimensional balls with finite or infinite radii. We provide characterization theorems for these classes, as well as Rudin’s type extension theorems for radial exponentially convex functions defined over n-dimensional balls into radial exponentially convex functions defined over the whole n-dimensional Euclidean space. We furthermore establish inversion theorems for the measures, termed here n-Nussbaum measures, associated with integral representations of radial exponentially convex functions. This in turn allows obtaining recurrence relations between 1-Nussbaum measures and n-Nussbaum measures for a given integer n greater than 1. We also provide a up to now unknown catalogue of radial exponentially convex functions and associated n-Nussbaum measures. We finally turn our attention into componentwise radial exponential convexity over product spaces, with a Rudin extension result and analytical examples of exponentially convex functions and associated Nussbaum measures. As a byproduct, we obtain a parametric model of nonseparable stationary space-time covariance functions that do not belong to the well-known Gneiting class.
Original language | British English |
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Article number | 28 |
Journal | Computational and Applied Mathematics |
Volume | 43 |
Issue number | 1 |
DOIs | |
State | Published - Feb 2024 |
Keywords
- Exponential convexity
- Integral representations
- Local stationarity
- Positive definite functions
- Rudin’s extensions