Fourier transforms in generalized Fock spaces (Q750831)

A generalisation of a classical Fock space has been defined and an extension of Fourier transform into the generalized Fock spaces has been developed. The author calls \(r^{pB}\) as an infinite dimensional Fock space. Some of the properties of these spaces were developed by the author [Applications of test surfunctions, Appl. Anal. 17, No.3, 169-185 (1984; Zbl 0525.46026)]. A comprehensive examination of the properties of the space \(r^{pB}\) and its dual \((r^{pB})'\) will be found in author's papers: J. Differ. equations 36, No.1, 74-88 (1980; Zbl 0407.46032); Appl. Anal. 24, 291-319 (1987; Zbl 0591.46038) and J. Math. Anal. Appl. 135, No.2, 432-461 (1988; Zbl 0681.46061).