On Kondratiev spaces of test functions in the non-Gaussian infinite-dimensional analysis (Q2877320)

The paper extends the approach to constructing Kondratiev spaces of test functions on a metric space \(Q\) developed (in the greatest generality) by \textit{Yu.\,M.\thinspace Berezans'kyi} and \textit{V.\,A.\thinspace Tesko} [Ukr.\ Mat.\ Zh.\ 55, No.\,12, 1587--1657 (2003), translated in Ukr.\ Math.\ J.\ 55, No.\,12, 1907--1979 (2003; Zbl 1080.46027)]. This approach uses the orthogonal basis given by a generating function \(Q\times H\ni (x,\lambda)\mapsto h(x,\lambda )\in \mathbb C\), where \(H\) is a complex Hilbert space, \(h\) satisfies certain assumptions (in particular, \(h(\cdot ,\lambda )\) is continuous, \(h(x,\cdot )\) is holomorphic at the origin). In the paper under review, the generating function is \(\gamma (\lambda )h(x,\alpha (\lambda ))\), where \(\gamma :\;H\to \mathbb C\) and \(\alpha :\;H\to H\) are holomorphic at the origin. Properties of the resulting spaces are investigated.