2024/02/01 by Riccardo Ghiloni, Ghiloni, Riccardo, Vincenzo Recupero +1
Mathematics · Computer Science · Physics and Astronomy · #Algebraic and Geometric Analysis #Matrix Theory and Algorithms #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.2402.00511
In the present paper, we prove a resolvent equation for the S-resolvent operator in the quaternionic framework. Exploiting this resolvent equation, we find a series expansion for the S-resolvent operator in an open neighborhood of any given quaternion belonging to the S-resolvent set. Some consequences of the series expansion are deduced. In particular, we describe a property of the geometry of the S-resolvent set in terms of the Cassini pseudo-metric on quaternions. The concept of vector-valued real analytic function of several variables plays a crucial role in the proof of the mentioned series expansion for the S-resolvent operator.