Recent zbMATH articles in MSC 46F12https://www.zbmath.org/atom/cc/46F122021-04-16T16:22:00+00:00WerkzeugGeneralized Schwartz type spaces and LCT based pseudodifferential operator.https://www.zbmath.org/1456.352492021-04-16T16:22:00+00:00"Jain, Pankaj"https://www.zbmath.org/authors/?q=ai:jain.pankaj"Kumar, Rajender"https://www.zbmath.org/authors/?q=ai:kumar.rajender"Prasad, Akhilesh"https://www.zbmath.org/authors/?q=ai:prasad.akhileshSummary: In connection with the LCT, in this paper, we define the Schwartz type spaces \(\mathcal{S}_{\Delta,\alpha,A} \), \(\mathcal{S}^{\Delta,\beta,B}\), \(\mathcal{S}^{\Delta,\beta,B}_{\Delta,\alpha,A} \), and study the mapping properties of LCT between these spaces. Moreover, we define a generalized \(\Delta\)-pseudo differential operator and investigate its mapping properties in the framework of the above Schwartz type spaces.Laplace transform of functions defined on a bounded interval.https://www.zbmath.org/1456.440022021-04-16T16:22:00+00:00"StankoviÄ‡, Bogoljub"https://www.zbmath.org/authors/?q=ai:stankovic.bogoljubSummary: Laplace transform \(\dot{\mathcal L}\) for functions belonging to \(L[0,b]\), \(0< b < \infty\) is defined. This definition is given by using the idea of \textit{H. Komatsu} [J. Fac. Sci., Univ. Tokyo, Sect. I A 34, 805--820 (1987; Zbl 0644.44001)] and [in: Structure of solutions of differential equations. Proceedings of the Taniguchi symposium, Katata, Japan, June 26--30, 1995 and the RIMS symposium, Kyoto, Japan, July 3--7, 1995. Singapore: World Scientific. 227--252 (1996; Zbl 0894.35005)] for Laplace hyperfunctions. As an application of \(\dot{\mathcal L}\) we solve an equation with fractional derivative and an integral equation of the first kind of convolution type.