Wavelet and Linear Algebra

Abstract In this paper‎, ‎we explore the properties of spectral functions from the perspective of convex analysis and monotone operator theory‎. ‎Specifically‎, ‎we examine the $\e$-subdifferential and $\e$-enlargement of a spectral function‎. ‎Also‎, ‎we study representative functions associated with the subdifferential of the spectral function‎. ‎In addition‎, ‎Fitzpatrick function has been studied due to its significance as one of the most important representative functions.

Abstract 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 engineering problems.