- The multiplier algebra of the noncommutative Schwartz space(arXiv)
Author : Tomasz Ciaś, Krzysztof Piszczek
Abstract : We describe the multiplier algebra of the noncommutative Schwartz space. This multiplier algebra can be seen as the largest ∗-algebra of unbounded operators on a separable Hilbert space with the classical Schwartz space of rapidly decreasing functions as the domain. We show in particular that it is neither a Q-algebra nor m-convex. On the other hand, we prove that classical tools of functional analysis, for example, the closed graph theorem, the open mapping theorem or the uniform boundedness principle, are still available
2. Existence of solutions to non-homogeneous higher order differential equation in the Schwartz space(arXiv)
Author : Valerii H. Samoilenko, Yuliia I. Samoilenko
Abstract : There is studied problem on existence of solutions to non-homogeneous differential equation of higher even order. Similar problem arises while studying soliton and soliton-like solutions to partial differential equations of integrable type. By means of Fourier transform and theory of pseudodifferential operators there is proved the theorem on necessary and sufficient conditions on existence of solutions to linear non-homogeneous differential equation of higher even order in the Schwartz space
