New Subclass of Meromorphic Functions Defined via Mittag–Leffler Function on Hilbert Space

In this paper, a novel class of meromorphic functions associated with the Mittag–Leffler function Eμ,ϑ(z) is introduced using the Hilbert space operator. In the punctured symmetric domain ⋓∗, essential properties of this class are systematically investigated. These properties include coefficient inequalities, growth and distortion bounds, as well as weighted and arithmetic mean estimates. Furthermore, the extreme points and radii of geometric properties such as close-to-convexity, starlikeness, and convexity are analyzed in detail. Additionally, the Hadamard product (or convolution) is explored to demonstrate the algebraic structure and stability of the introduced function class under this operation. Integral mean inequalities are also established to provide further insights into the behavior of these functions within the given domain.