Lee, Kyoung Sim Gel’fand triples associated with finite dimensional Gaussian measure. (English) Zbl 0858.46034 Soochow J. Math. 22, No. 1, 1-16 (1996). Summary: Recently, Kubo and Kuo have characterized the finite-dimensional Hida distributions in \(({\mathcal S})^*\). In the characterization, they have introduced the finite-dimensional Gel’fand triple \({\mathcal H}(\mathbb{R}^k)\subset {\mathcal H}_0(\mathbb{R}^k)\subset {\mathcal H}^*(\mathbb{R}^k)\). We construct a new Gel’fand triple \({\mathcal H}^\beta(\mathbb{R}^k)\subset {\mathcal H}^0_0(\mathbb{R}^k)\subset ({\mathcal H}^\beta)^*(\mathbb{R}^k)\) for \(0\leq \beta<1\) and generalize some of their results. In particular, we will generalize the characterization theorems for the spaces \({\mathcal H}^*(\mathbb{R}^k)\) and \({\mathcal H}(\mathbb{R}^k)\) to the spaces \(({\mathcal H}^\beta)^*(\mathbb{R}^k)\) and \({\mathcal H}^\beta(\mathbb{R}^k)\). The Fourier transform is also extended to the space \(({\mathcal H}^\beta)^*(\mathbb{R}^k)\) for further study of the finite-dimensional distribution theory. MSC: 46F25 Distributions on infinite-dimensional spaces 46F10 Operations with distributions and generalized functions 42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type 47A70 (Generalized) eigenfunction expansions of linear operators; rigged Hilbert spaces Keywords:finite-dimensional Hida distributions in \(({\mathcal S})^*\); Gel’fand triple; characterization; Fourier transform PDFBibTeX XMLCite \textit{K. S. Lee}, Soochow J. Math. 22, No. 1, 1--16 (1996; Zbl 0858.46034)