Approximating Functions of Positive Compact Operators by Using Bell Polynomials

Abstract

After recalling the most important properties of the Bell polynomials, we show how to approximate a positive compact operator by a suitable matrix. Then, we derive a representation formula for functions of the obtained matrix, which can be considered as an approximate value for the functions of the corresponding operator.

Keywords

• resolvent
• Bell polynomials
• orthogonal invariants
• Robert’s formulas
• positive compact operators
• matrix functions