Linear Operators: Spectral theory |
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Page 948
... R is dense in S , and that coincides . with on R , we conclude immediately that 808 , 81 → Sq S2s , and = $ 1 ( 8283 ) = ( 8182 ) 83 . = It remains to be shown that inverse elements under exist in S. Consider the mapping H : AP → AP ...
... R is dense in S , and that coincides . with on R , we conclude immediately that 808 , 81 → Sq S2s , and = $ 1 ( 8283 ) = ( 8182 ) 83 . = It remains to be shown that inverse elements under exist in S. Consider the mapping H : AP → AP ...
Page 1159
... of R into R. space Next we shall show that κ ( R ) is dense in the R. If not , then by applying Lemma 4.2 to R , we find that there exists a function L2 ( R ) with H20 but such that H vanishes on κ ( R ) . T1H € L2 ( R ) it follows from ...
... of R into R. space Next we shall show that κ ( R ) is dense in the R. If not , then by applying Lemma 4.2 to R , we find that there exists a function L2 ( R ) with H20 but such that H vanishes on κ ( R ) . T1H € L2 ( R ) it follows from ...
Page 1579
... To ( r - 17 ) : L2 ( I , r ) → L2 ( I , r ) -1 is symmetric , and that its adjoint is T1 ( r - 1t , r ) . l ( b ) ... To ( r - 1 / 2tr - 1 / 2 ) is bounded below as an operator in L2 ( I , r ) if and only if To ( r - 1 / 2 tr − 1 / 2 ) ...
... To ( r - 17 ) : L2 ( I , r ) → L2 ( I , r ) -1 is symmetric , and that its adjoint is T1 ( r - 1t , r ) . l ( b ) ... To ( r - 1 / 2tr - 1 / 2 ) is bounded below as an operator in L2 ( I , r ) if and only if To ( r - 1 / 2 tr − 1 / 2 ) ...
Contents
BAlgebras | 859 |
Bounded Normal Operators in Hilbert Space | 887 |
Miscellaneous Applications | 937 |
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adjoint extension adjoint operator algebra analytic B-algebra B*-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure Co(I coefficients complex numbers converges Corollary deficiency indices Definition denote dense domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Haar measure Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval kernel L₁(R L₂(I L₂(R Lemma Let f linearly independent mapping Math matrix measure neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive preceding lemma prove real axis real numbers representation satisfies Section sequence solution spectral spectral theory square-integrable subspace Suppose symmetric operator T₁ T₂ theory To(t topology unique unitary vanishes vector zero