Linear Operators: Spectral theory |
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Page 1120
... assume for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces . Thus , the key to the situation that we wish to analyze is the ...
... assume for simplicity of statement that Hilbert space is separable . Subdiagonal representations of an operator are connected with the study of its invariant subspaces . Thus , the key to the situation that we wish to analyze is the ...
Page 1594
... assume ( a ) the function g is non - negative and piecewise continuous in the interval [ 0 , ∞ ) , ( b ) the ... assume that lim Q ( t ) === ∞ . t - b ( 8 ) ( 7.67 ) In the interval [ a , b ) , let Q be defined as in ( 7 ) , and assume ...
... assume ( a ) the function g is non - negative and piecewise continuous in the interval [ 0 , ∞ ) , ( b ) the ... assume that lim Q ( t ) === ∞ . t - b ( 8 ) ( 7.67 ) In the interval [ a , b ) , let Q be defined as in ( 7 ) , and assume ...
Page 1595
... Assume that Sop ( t ) -1/2 dt ∞ , lim Q ( t ) = = c . t - b Then the essential spectrum of 7 is the half - line [ c , ∞ ) ( 7.66 ) . ( 12 ) In the interval [ a , b ) let t Z ( t ) = q ( t ) + 4p ( s ) a ( [ p ( s ) 2 -1 ( s ) -1ds and ...
... Assume that Sop ( t ) -1/2 dt ∞ , lim Q ( t ) = = c . t - b Then the essential spectrum of 7 is the half - line [ c , ∞ ) ( 7.66 ) . ( 12 ) In the interval [ a , b ) let t Z ( t ) = q ( t ) + 4p ( s ) a ( [ p ( s ) 2 -1 ( s ) -1ds and ...
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