A multiplicative convolution on the spectra of algebras of symmetric analytic functions

Symmetric Polynomials and Holomorphic Functions on Infinite Dimensional Spaces

“…THE CASE OF 1 [8] In this section we consider the algebra H bs ( 1 ). In addition to the basis {F n }, this algebra has a different natural basis that is given by the sequence {G n } :…”

On Algebraic Basis of the Algebra of Symmetric Polynomials on lp(Cn)

“…Algebras of polynomials and analytic functions on a Banach space which are invariant (symmetric) with respect to a group of linear operators ( ) acting on were studied by a number of authors [1][2][3][4][5][6][7][8][9][10] (see also a survey [11]). If has a symmetric structure, then it is natural to consider the case when ( ) is a group of operators which preserve this structure.…”

Homomorphisms of the algebra of symmetric analytic functions on $\ell_1$

“…Recall that for any ϕ, θ ∈ M bs (ℓ p ) and f ∈ H bs (ℓ p ), the symmetric convolution ϕ ⋆ θ was defined in [4] as follows c Chernega I., 2014 where…”

“….). In [6] the multiplicative intertwining of x and y, x ⋄ y, was defined as the resulting sequence of ordering the set {x i y j : i, j ∈ N} with one single index in some fixed order. It enabled us to define the multiplicative convolution operator as a mapping f → M y ( f ), where M y ( f )(x) = f (x ⋄ y).…”

“…It enabled us to define the multiplicative convolution operator as a mapping f → M y ( f ), where M y ( f )(x) = f (x ⋄ y). And for arbitrary ϕ, θ ∈ M bs (ℓ p ) in [6] it was defined their multiplicative convolution ϕ♦θ according to…”