Generalized Integral Operators and Schwartz Kernel Theorem
arXiv:math/0403312 · doi:10.1016/j.jmaa.2005.01.006
Abstract
In connection with the classical Schwartz kernel theorem, we show that in the framework of Colombeau generalized functions a large class of linear mappings admit integral kernels. To do this, we need to introduce news spaces of generalized functions with slow growth and the corresponding adapted linear mappings. Finally, we show that in some sense Schwartz' result is contained in our main theorem.
18 pages
References in corpus (1)
Cited by in corpus (7)
- Microlocal analysis in the dual of a Colombeau algebra: generalized wave front sets and noncharacteristic regularity
- Regular rapidly decreasing nonlinear generalized functions. Application to microlocal regularity
- Mathematical problems on generalized functions and the canonical Hamiltonian formalism
- Generalized Oscillatory Integrals and Fourier Integral Operators
- Kernel Theorems in Spaces of Tempered Generalized Functions
- On the composition of integral operators acting in tempered Colombeau algebras
- Topological properties of regular generalized function algebras