Linear Operators, Part 2 |
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Page 970
If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in L ( R ) , L ( R ) and f is the limit in the norm of L ( R ) of the generalized sequence zef } . Hence , by Theorem 9 , of is the ...
If Xe denotes the characteristic function of the set e in E , and if f is in L2 ( R ) , then Xef is in L ( R ) , L ( R ) and f is the limit in the norm of L ( R ) of the generalized sequence zef } . Hence , by Theorem 9 , of is the ...
Page 976
It is easily seen that this theorem asserts that if f is in L2 ( R " ) , the limit + N gt , ... , tn ) = ( 29 ) - " / 2 lim -n + N elima S M2 .... , in ) -N -N • exp { -i ( txi + ... + tnxn ) } dxz ... dxn exists in the norm of L2 ( R ...
It is easily seen that this theorem asserts that if f is in L2 ( R " ) , the limit + N gt , ... , tn ) = ( 29 ) - " / 2 lim -n + N elima S M2 .... , in ) -N -N • exp { -i ( txi + ... + tnxn ) } dxz ... dxn exists in the norm of L2 ( R ...
Page 1124
If En , E are in F and q ( En ) increases to the limit ( E ) , then it follows from what we have already proved that E , is an increasing sequence of projections and En 5E . If E. is the strong limit of En , then E SE and q ( EQ ) = Q ...
If En , E are in F and q ( En ) increases to the limit ( E ) , then it follows from what we have already proved that E , is an increasing sequence of projections and En 5E . If E. is the strong limit of En , then E SE and q ( EQ ) = Q ...
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Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
Copyright | |
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