Cruz-Báez, Domingo Israel; Rodríguez Expósito, José New inversion formulas for the Krätzel transformation. (English) Zbl 0989.46026 Int. J. Math. Math. Sci. 25, No. 4, 253-263 (2001). A generalization of the well-known Meijer transform introduced and denoted by \(K^0_\nu\) by E. Krätzel [see “Generalized functions and operational calculus, Proc. Conf., Varna, 1975, 148-155, Bulgar. Acad. Sci., Sofia (1979; Zbl 0403.44003); see also E. Krätzel and H. Menzer, Publ. Math. Debrecen 18 (1971), 139-147 (1972; Zbl 0247.33014)] is analyzed by the authors applying the kernel method on the Schwartz space of distributions \({\mathcal E}(I)\). Several properties, namely, analyticity, boundedness and an inversion theorem are established for the generalized transformation on the dual space \({\mathcal E}'(I)\). As a particular case, another inversion formula for the Meijer transform is also derived. Reviewer: Nácere Hayek (La Laguna) Cited in 1 Document MSC: 46F12 Integral transforms in distribution spaces 44A15 Special integral transforms (Legendre, Hilbert, etc.) Keywords:Meijer transform; kernel method; Schwartz space of distributions; analyticity; boundedness; inversion theorem; inversion formula Citations:Zbl 0403.44003; Zbl 0247.33014 PDFBibTeX XMLCite \textit{D. I. Cruz-Báez} and \textit{J. Rodríguez Expósito}, Int. J. Math. Math. Sci. 25, No. 4, 253--263 (2001; Zbl 0989.46026) Full Text: DOI EuDML