This article studies the properties of positive definite, radial functions on free groups following work Haagerup and Knudby [Proc. Amer. Math. Soc. 143 (2015), pp. 1477–1489]. We obtain characterizations with respect to ℓ<...

In this paper, we give a fundamental convexity preserving for spectral functions. Indeed, we investigate infimal convolution, Moreau envelope and proximal average for convex spectral functions, and show that this properties are inherited from the properties of its corresponding convex function. This results have many applications in Applied Mathematics such as semi-definite programmings and eng...

This paper delves into the extension and characterization of radial positive definite functions non-integer dimensions. We provide a thorough investigation by employing Riemann–Liouville fractional integral Caputo derivatives, enabling comprehensive understanding these functions. Additionally, we introduce secondary based on Bernstein completely monotone The practical significance our study is ...