Tuesday 6 January 2015

Operator Algebra Note 4 Frame Operator / April 2, 2008

Operator Algebra

Note 4
Frame Operator 

TANAKA Akio


1
Hilbert space     H
Sequence of points in H     {xn}
Certain constants     0 <  B <    
x  H
A ||x||2 |<xxn>|2  ||x||2
{xn} is frame.
A is lower bound.
B is upper bound.
2
x  H
<xxn>||xn|| is convergent.
S : x  <xxn>xsatisfies S B.
is frame operator.

[References]
Frame / Tokyo February 27, 2005
More details, Quantum Theory for Language Map 1
Frame-Quantum Theory / Tokyo March 12, 2005
More details, Frame-Quantum Theory Map 2


Tokyo April 2, 2008

Sekinan Research Field of Language

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