Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 893
Let E be a bounded self adjoint spectral measure in Hilbert space defined on a field of subsets of a set S. Then the map † T ( ) defined by the equation T ( 4 ) = st ( 8 ) E ( ds ) , fe B ( S , E ) , is a continuous * -homomorphic map ...
Let E be a bounded self adjoint spectral measure in Hilbert space defined on a field of subsets of a set S. Then the map † T ( ) defined by the equation T ( 4 ) = st ( 8 ) E ( ds ) , fe B ( S , E ) , is a continuous * -homomorphic map ...
Page 900
1 and thus there is a bounded function to on S with f ( s ) = to ( s ) except for s in a set having E measure zero . If f is E - measurable then to is a bounded E - measurable function , i.e. , an element of the B * -algebra BS , E ) .
1 and thus there is a bounded function to on S with f ( s ) = to ( s ) except for s in a set having E measure zero . If f is E - measurable then to is a bounded E - measurable function , i.e. , an element of the B * -algebra BS , E ) .
Page 1240
Semi - bounded Symmetric Operators In this section we study the self adjoint extensions of those operators in a class of symmetric operators which arise frequently from the boundary value problems of mathematical physics .
Semi - bounded Symmetric Operators In this section we study the self adjoint extensions of those operators in a class of symmetric operators which arise frequently from the boundary value problems of mathematical physics .
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