Measurable functionals and finitely absolutely continuous measures on Banach spaces (Q2722149)

Let \(B\) be a separable Banach space, and let \(\mu\) be a probability measure on the \(\sigma\)-algebra of the Borel subsets of \(B.\) The author investigates properties of measurable polynomials with respect to the measure \(\mu\) and to the corresponding orthogonal expansions of polynomials square integrable with respect to the measure \(\mu\) and other probabilistic measures. In other words, some measures are considered as the generalized functionals on the space \((B, \mu)\) with measure \(\mu.\) The structure of orthogonal polynomials in the space \(L_{2}(B, \mu)\) for probabilistic measure \(\mu\) on the Banach space is investigated. These polynomials are described in terms of the Hilbert-Schmidt kernels on a space of square integrable linear functionals.