Representation of spectra of algebras of block-symmetric analytic functions of bounded type

Abstract

The paper contains a description of symmetric convolution of the algebra of block-symmetric analytic functions of bounded type on $\ell_{1}$-sum of the space $\mathbb{C}^{2}.$ We show that the specrum of such algebra does not coincide of point evaluation functionals and described characters of the algebra as functions of exponential type with plane zeros.

Keywords

• algebraic basis
• block-symmetric polynomials
• block-symmetric analytic functions
• spectrum
• symmetric intertwining
• symmetric convolution