Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |
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Page 1224
1 2 1 2 1 2 2 = 1 > 2 ( b ) If T is symmetric then every symmetric extension T , of Tj ; and , in particular , every self adjoint extension of Tı , satisfies Ti CT , CT CT * Proof . If T , CT , and ye D ( T * ) , then ( x , T * y ) ...
1 2 1 2 1 2 2 = 1 > 2 ( b ) If T is symmetric then every symmetric extension T , of Tj ; and , in particular , every self adjoint extension of Tı , satisfies Ti CT , CT CT * Proof . If T , CT , and ye D ( T * ) , then ( x , T * y ) ...
Page 1236
A set of boundary conditions B ( x ) = 0 , i = 1 , ... , k , is 0 said to be symmetric if the equations B ; ( x ) = B ... Every closed symmetric extension of T is the restriction of 1 * to the subspace of D ( T * ) determined by a ...
A set of boundary conditions B ( x ) = 0 , i = 1 , ... , k , is 0 said to be symmetric if the equations B ; ( x ) = B ... Every closed symmetric extension of T is the restriction of 1 * to the subspace of D ( T * ) determined by a ...
Page 1272
Maximal symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has ...
Maximal symmetric operators . If T is a symmetric operator with dense domain , then it has proper symmetric extensions provided both of its deficiency indices are different from zero . A maximal symmetric operator is one which has ...
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