Linear Operators: Spectral theory |
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Page 1092
... finite number N of non - zero eigenvalues , we write λ , ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
... finite number N of non - zero eigenvalues , we write λ , ( T ) = 0 , n > N ) . Then , for each positive integer m ... finite- dimensional range , it is enough to prove the lemma in the special case that T has finite - dimensional domain ...
Page 1460
... finite below 2 , and the leading coefficient of t + t1 never vanishes , T + T1 is finite below 2 . .... - PROOF . It is clear that we may suppose without loss of generality that 20. By Corollary 24 ( b ) , Corollary XI1.4.13 , and ...
... finite below 2 , and the leading coefficient of t + t1 never vanishes , T + T1 is finite below 2 . .... - PROOF . It is clear that we may suppose without loss of generality that 20. By Corollary 24 ( b ) , Corollary XI1.4.13 , and ...
Page 1913
... finite , III.4.3 ( 126 ) Lebesgue extension of , III.5.18 ( 143 ) as a metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite measure spaces , III.11.3 ( 186 ) of finite number of o ...
... finite , III.4.3 ( 126 ) Lebesgue extension of , III.5.18 ( 143 ) as a metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite measure spaces , III.11.3 ( 186 ) of finite number of o ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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adjoint extension adjoint operator algebra analytic B-algebra Borel set boundary conditions boundary values bounded operator C₁ closed closure coefficients compact operator complex numbers continuous function converges Corollary deficiency indices Definition denote dense eigenvalues element equation essential spectrum Exercise exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function defined function f Hence Hilbert space Hilbert-Schmidt operator identity inequality integral interval isometric isomorphism kernel L₁ L₁(R L₂(I L₂(R Lemma Let f linear linearly independent mapping matrix measure neighborhood non-zero norm open set operators in Hilbert orthogonal orthonormal basis Plancherel's theorem positive preceding lemma PROOF prove real axis satisfies sequence solution spectral spectral theorem square-integrable subset subspace Suppose T₁ T₁(t T₂ theory To(t topology tr(T unique unitary vanishes vector zero