"The matrix representation of unbounded operators using sequences"Shamsabadi, MitraIn many applications such as acoustics and vibration simulation some bounded operator equations that can not be treated analytically but should be solved numerically, where the matrix representation of bounded operators play a key role. Lastly, this theory has extended using some various frames. On the other hand, dealing with unbounded operators is, naturally, more complicated and adds technicalities compared to bounded operators. This is, in particular, true for their matrix representations. It is well-known in physics that such representations with orthonormal bases does not work well. In this paper, we will address this issue and interpret an unbounded operator by using some frame-related sequences with more naturally linked to unboundedness. It can be shown that the matrix representation of a closed operator $O$ using two sequences $\Phi$ and $\Psi$ can be as an extension of $C_{\Phi}OD_{\Psi}$. Also, we will state its adjoint and inverse operators (if there exist) with some conditions can be interpreted as a matrix representation of an operator again. |
« back