Linear Operators: Spectral theory |
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Page 1027
... belongs to the spectrum of both T and ET . Suppose that 10 belongs to the spectrum of T. Since T is compact , Theorem VII.4.5 shows that λ is an eigenvalue and hence for some non - zero x in § we have Tx λπ , and hence , since T TE , we ...
... belongs to the spectrum of both T and ET . Suppose that 10 belongs to the spectrum of T. Since T is compact , Theorem VII.4.5 shows that λ is an eigenvalue and hence for some non - zero x in § we have Tx λπ , and hence , since T TE , we ...
Page 1116
... belongs to the Hilbert - Schmidt class C2 . If we let Ap = y - p / 2p , then 4 is plainly self adjoint and A belongs A to the class C ,, where r ( 1 - p / 2 ) = p , i.e. , r = p ( 1 − p / 2 ) -1 . Thus , by Lemma 9 , TBA belongs to the ...
... belongs to the Hilbert - Schmidt class C2 . If we let Ap = y - p / 2p , then 4 is plainly self adjoint and A belongs A to the class C ,, where r ( 1 - p / 2 ) = p , i.e. , r = p ( 1 − p / 2 ) -1 . Thus , by Lemma 9 , TBA belongs to the ...
Page 1602
... belongs to the essential spectrum of 7 ( Hartman and Wintner [ 14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let f be a real solution of the equation ( 2-7 ) = 0 on [ 0 , ∞ ) which is not square - integrable but ...
... belongs to the essential spectrum of 7 ( Hartman and Wintner [ 14 ] ) . ( 48 ) Suppose that the function q is bounded below , and let f be a real solution of the equation ( 2-7 ) = 0 on [ 0 , ∞ ) which is not square - integrable but ...
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