Mathematics – Functional Analysis
Scientific paper
2008-12-19
Mathematics
Functional Analysis
39 pages
Scientific paper
In this work we develop a theory of Vessels. This object arises in the study of overdetermined 2D systems invariant in one of the variables, which are usually called time invariant. To each overdetermined time invariant 2D systems there is associated a vessel, which is a collection of system operators satisfying certain relations and vise versa. Such an invariance forces the theory of vessels to resemble a constant (classical) 1D case and as a result many notions are naturally redefined and most theorems are reproved in this setting. The notion of transfer function and its connection to the overdetermined 2D time invariant system (and the corresponding vessel) is one of the topics of this work. It is well known that multiplicative structure of a transfer function of a 1D system is closely connected to the decomposition of the state space into invariant subspaces of the state operator and we generalize this result to a wider class of functions. This class (denoted by $\boldsymbol {\mathcal I}$) arises as a class of transfer functions, which intertwine solutions of ODEs with spectral parameters. At the end we present solution of factorization problems for finite dimensional case.
Melnikov Andrey
Vinnikov Victor
No associations
LandOfFree
Overdetermined 2D Systems Invariant in One Direction and Their Transfer Functions does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Overdetermined 2D Systems Invariant in One Direction and Their Transfer Functions, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Overdetermined 2D Systems Invariant in One Direction and Their Transfer Functions will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-727053