Linear Operators: Spectral theory |
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Page 984
The set of functions f in Ly ( R ) for which s vanishes in a neighborhood of infinity
is dense in Ly ( R ) . Proof . It follows from Lemma 3 . 6 that the set of all functions
in L2 ( R , B , u ) which vanish outside of compact sets is dense in this space ...
The set of functions f in Ly ( R ) for which s vanishes in a neighborhood of infinity
is dense in Ly ( R ) . Proof . It follows from Lemma 3 . 6 that the set of all functions
in L2 ( R , B , u ) which vanish outside of compact sets is dense in this space ...
Page 993
It remains to be proved that the number ay is independent of the open set V . If f is
in Lj ( R ) L2 ( R ) , f vanishes on the complement of V , and f ( m ) = 1 for m in an
open subset V , of V , then the above proof shows that ( 0f ) ( m ) = Qy for every ...
It remains to be proved that the number ay is independent of the open set V . If f is
in Lj ( R ) L2 ( R ) , f vanishes on the complement of V , and f ( m ) = 1 for m in an
open subset V , of V , then the above proof shows that ( 0f ) ( m ) = Qy for every ...
Page 997
Since of is in L ( R ) , L ( R ) whenever f is , it follows that Ø maps each function in
L ( R ) , L ( R ) into a continuous function on R which vanishes at Poo . 23
THEOREM . Let y be a bounded measurable function on R . Then a point m , in Ř
is in ...
Since of is in L ( R ) , L ( R ) whenever f is , it follows that Ø maps each function in
L ( R ) , L ( R ) into a continuous function on R which vanishes at Poo . 23
THEOREM . Let y be a bounded measurable function on R . Then a point m , in Ř
is in ...
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Contents
IX | 859 |
Eigenvalues and Eigenvectors | 903 |
Spectral Representation | 911 |
Copyright | |
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