Linear Operators: Spectral theory |
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Page 1900
... definition , IV.2.25 ( 242 ) remarks concerning , ( 386–387 ) study of , IV.7 Almost uniform ( or μ - uniform conver- gence ) definition , III . 6.1 ( 145 ) . ( See also Convergence of func- tions ) Analytic continuation , ( 230 ) ...
... definition , IV.2.25 ( 242 ) remarks concerning , ( 386–387 ) study of , IV.7 Almost uniform ( or μ - uniform conver- gence ) definition , III . 6.1 ( 145 ) . ( See also Convergence of func- tions ) Analytic continuation , ( 230 ) ...
Page 1907
... definition , VII.1.2 ( 556 ) , VII.11 ( 606 ) , X.3.1 ( 902 ) Eigenvector , definition , VII.1.2 ( 556 ) , X.3.1 ( 903 ) Embedding , natural , of a B - space into its second conjugate , II.3.18 ( 66 ) End point of an interval , III.5.15 ...
... definition , VII.1.2 ( 556 ) , VII.11 ( 606 ) , X.3.1 ( 902 ) Eigenvector , definition , VII.1.2 ( 556 ) , X.3.1 ( 903 ) Embedding , natural , of a B - space into its second conjugate , II.3.18 ( 66 ) End point of an interval , III.5.15 ...
Page 1921
... definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11- 12 ( 512-513 ) Strong topology , in a normed space , II.3.1 ( 59 ) , ( 419 ) Structure space of a B - algebra ...
... definition , VII.7 ( 458 ) Strong operator topology , definition , VI.1.2 ( 475 ) properties , VI.9.1–5 ( 511 ) , VI.9.11- 12 ( 512-513 ) Strong topology , in a normed space , II.3.1 ( 59 ) , ( 419 ) Structure space of a B - algebra ...
Contents
BAlgebras | 859 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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A₁ 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 countably deficiency indices Definition denote dense eigenfunctions eigenvalues element equation essential spectrum Exercise exists f₁ finite dimensional follows from Lemma follows from Theorem formal differential operator formally self adjoint formula Fourier function f Haar measure Hence Hilbert space Hilbert-Schmidt operator homomorphism identity inequality infinity integral interval kernel L₁ L₁(R L₂ L₂(I L₂(R Lemma Let f linearly independent mapping matrix measure neighborhood non-zero norm operators in Hilbert orthogonal Plancherel's theorem positive preceding lemma prove real axis real numbers satisfies sequence shows solution spectral set spectral theorem square-integrable subset subspace Suppose T₁ T₂ theory To(t topology tr(T transform uniformly unique unitary vanishes vector zero