Power operations and differentiations associated with supersymmetric polynomials on a Banach space

Abstract

We consider different approaches to constructing power operations on the ring of multisets associated with supersymmetric polynomials of infinitely many variables. Some relations between constructed power operations are established. Also, we study differential operators on algebras of symmetric and supersymmetric analytic functions of bounded type on the Banach space of absolutely summable sequences. We have proved the continuity of such operators and found their evaluations on basis polynomials.

Keywords

• supersymmetric polynomial
• analytic function on a banach space
• power operation
• differential operator
• ring of multisets