The structure of closed ideals of a regular algebra containing the classical A∞ is considered. Several division and approximation results are proved and a characterization of those ideals whose intersection with A∞ is not {0} is obtained. A complete description of the ideals with countable hull is given, with applications to synthesis of hyperfunctions.
he paper is devoted to investigation of Gegenbauer white noise functionals. A particular attention is paid to the construction of the infinite dimensional Gegenbauer white noise measure , via the Bochner-Minlos theorem, on a suitable nuclear triple. Then we give the chaos decomposition of the L²-space with respect to the measure by using the so-called β-type Wick product.
Let denote the real-valued functions continuous on the extended real line and vanishing at . Let denote the functions that are left continuous, have a right limit at each point and vanish at . Define to be the space of tempered distributions that are the th distributional derivative of a unique function in . Similarly with from . A type of integral is defined on distributions in and . The multipliers are iterated integrals of functions of bounded variation. For each , the spaces...