Linear Operators: Spectral theory |
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Page 1913
... space , discrete case in B - space , VIII.5.1-4 ( 661-662 ) in L1 , VIII.5.5 ( 662 ) in L , VIII.5.9 ( 667 ) Mean ... metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite ...
... space , discrete case in B - space , VIII.5.1-4 ( 661-662 ) in L1 , VIII.5.5 ( 662 ) in L , VIII.5.9 ( 667 ) Mean ... metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of finite number of finite ...
Page 1914
... space , II.3.18 ( 66 ) Natural homomorphism onto factor space , ( 38 ) , ( 39 ) Neighborhood , ɛ- , in a metric space , 1.6.1 ( 18 ) fundamental family of , I.4.6 ( 10 ) of a point or set , I.4.1 ( 10 ) Nikodým . ( See also Radon ...
... space , II.3.18 ( 66 ) Natural homomorphism onto factor space , ( 38 ) , ( 39 ) Neighborhood , ɛ- , in a metric space , 1.6.1 ( 18 ) fundamental family of , I.4.6 ( 10 ) of a point or set , I.4.1 ( 10 ) Nikodým . ( See also Radon ...
Page 1921
... space , definition , VII.7 ( 458 ) Strictly convex B - space , definition , VII.7 ( 458 ) Strong operator topology ... metric , definition , I.6.1 ( 18 ) metric or strong , in a B - space , ( 419 ) study of , 1.6 norm or strong , in a ...
... space , definition , VII.7 ( 458 ) Strictly convex B - space , definition , VII.7 ( 458 ) Strong operator topology ... metric , definition , I.6.1 ( 18 ) metric or strong , in a B - space , ( 419 ) study of , 1.6 norm or strong , in a ...
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