Linear Operators: Spectral theory |
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Page 1188
... assumed that D ( T ) is dense . Similarly whenever the inverse T - 1 is mentioned it is tacitly assumed that T is one - to - one . We recall that the orthocomplement of a set 2 in 5 is defined as the set { xx € H , ( x , A ) = 0 } ...
... assumed that D ( T ) is dense . Similarly whenever the inverse T - 1 is mentioned it is tacitly assumed that T is one - to - one . We recall that the orthocomplement of a set 2 in 5 is defined as the set { xx € H , ( x , A ) = 0 } ...
Page 1593
... assumed to be real and continuous , and p is assumed to be positive . The following statements describe situations in which the essen- tial spectrum is void : ( 1 ) For some ( real or complex ) 2 , the equation ( 2 − t ) f = 0 has two ...
... assumed to be real and continuous , and p is assumed to be positive . The following statements describe situations in which the essen- tial spectrum is void : ( 1 ) For some ( real or complex ) 2 , the equation ( 2 − t ) f = 0 has two ...
Page 1596
... assumed that 7 is bounded below ( cf. the exercises in Section 9.D ) . Additional criteria are given below for the more special operator d \ 2 T = + g ( t ) dt where the function q is assumed to be real and continuous . The following ...
... assumed that 7 is bounded below ( cf. the exercises in Section 9.D ) . Additional criteria are given below for the more special operator d \ 2 T = + g ( t ) dt where the function q is assumed to be real and continuous . The following ...
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