Let $l^2(Bbb Z)$ be the Hilbert space of square summable double
sequences of complex numbers with standard basis ${e_n:ninBbb
Z}$, and let us consider a bounded matrix $A$ on $l^2(Bbb Z)$
satisfying the following system of equations
egin{itemize}
item[1.] $lan
Ae_{2j},e_{2i}
an=p_{ij}+alan Ae_{j},e_i
an$;
item[2.] $lan
Ae_{2j},e_{2i-1}
an=q_{ij}+blan Ae_{j},e_{i}
an$;
item[3.] $lan
Ae_{2j-1},e_{2i}
an=v_{ij}+clan Ae_{j},e_{i}
an$;
item[4.] $lan
Ae_{2j-1},e_{2i-1}
an=w_{ij}+dlan Ae_{j},e_{i}
an$
end{itemize}
for all $i,j$, where $P=(p_{ij})$, $Q=(q_{ij})$, $V=(v_{ij})$,
$W=(w_{ij})$ are bounded matrices on $l^2(Bbb Z)$ and
$a,b,c,dinBbb C$.
par
It is clear that the solutions of the above system of equations
introduces a class of infinite matrices whose entries are related
``dyadically". In cite{Ho:g}, it is shown that the seemingly
complicated task of constructing these matrices can be carried out
alternatively in a systematical and relatively simple way by
applying the theory of Hardy classes of operators through certain
operator equation on ${cal B}({cal H})$ (space of bounded
operators on $cal H$) induced by a shift. Our purpose here is to
present explicit formula for the homogeneous solutions this equation.
| Identifer | oai:union.ndltd.org:NSYSU/oai:NSYSU:etd-0120112-224934 |
| Date | 20 January 2012 |
| Creators | Wang, Tsung-Chieh |
| Contributors | Jen-Chih Yao, Mark C. Ho, Chun-Yen Chou, Jyh-Shyang Jeang |
| Publisher | NSYSU |
| Source Sets | NSYSU Electronic Thesis and Dissertation Archive |
| Language | English |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | http://etd.lib.nsysu.edu.tw/ETD-db/ETD-search/view_etd?URN=etd-0120112-224934 |
| Rights | unrestricted, Copyright information available at source archive |
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