Linear Operators: Spectral theory |
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Page 1279
... interval of the real axis . The interval I can be open , half - open , or closed . The interval [ a , ∞ ) is considered to be half - open ; the interval ( ∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
... interval of the real axis . The interval I can be open , half - open , or closed . The interval [ a , ∞ ) is considered to be half - open ; the interval ( ∞ , ∞ ) to be open . Thus a closed interval is a compact set . An end point t ...
Page 1539
... interval [ 0 , ∞ ) . Prove that a complex number λ belongs to the essential spectrum of 7 if and only if there exists a sequence { f } of functions in D ( To ( 7 ) ) such that \ ƒ „ | = 1 , ƒ „ vanishes in the interval [ 0 , n ] , and ...
... interval [ 0 , ∞ ) . Prove that a complex number λ belongs to the essential spectrum of 7 if and only if there exists a sequence { f } of functions in D ( To ( 7 ) ) such that \ ƒ „ | = 1 , ƒ „ vanishes in the interval [ 0 , n ] , and ...
Page 1599
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of 7 ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
... interval [ 0 , ∞ ) . Then on the positive real axis every interval of length K contains a point of the essential spectrum of 7 ( Glazman [ 4 ] , Exercise 9.A 6 ) . ( 32 ) On the interval [ 0 , ∞ ) , if q ( t ) tends monotonically to ...
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