Linear Operators: Spectral theory |
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Page 1791
... ergodic theorem . Duke Math . J. 5 , 19–20 ( 1939 ) . 8. An ergodic theorem for general semi - groups . Proc . Nat . Acad . Sci . U.S.A. 25 , 625-627 ( 1939 ) . Birkhoff , G. , and MacLane , S. 1. A survey of modern algebra . Macmillan ...
... ergodic theorem . Duke Math . J. 5 , 19–20 ( 1939 ) . 8. An ergodic theorem for general semi - groups . Proc . Nat . Acad . Sci . U.S.A. 25 , 625-627 ( 1939 ) . Birkhoff , G. , and MacLane , S. 1. A survey of modern algebra . Macmillan ...
Page 1859
... ergodic theorems , I , II . I. Generalized ergodic theorems . Studia Math . 12 , 65–73 ( 1951 ) . II . Ergodic theory of continued fractions . ibid . 12 , 74-79 ( 1951 ) . Saks , S. ( see also Banach , S. ) 1 . 2 . 3 . 4 . 5 . Theory of ...
... ergodic theorems , I , II . I. Generalized ergodic theorems . Studia Math . 12 , 65–73 ( 1951 ) . II . Ergodic theory of continued fractions . ibid . 12 , 74-79 ( 1951 ) . Saks , S. ( see also Banach , S. ) 1 . 2 . 3 . 4 . 5 . Theory of ...
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... Theory IV.3 Finite VI.2 Dimensional Spaces Adjoints VII.4 Spectra of Compact Operators V.8 Extremal Points VI.10 Riesz Convexity Theorem . VII.6 Perturbation Theory VIII.8 Uniform Ergodic Theory VII.9 Functions of Unbounded Operators IV ...
... Theory IV.3 Finite VI.2 Dimensional Spaces Adjoints VII.4 Spectra of Compact Operators V.8 Extremal Points VI.10 Riesz Convexity Theorem . VII.6 Perturbation Theory VIII.8 Uniform Ergodic Theory VII.9 Functions of Unbounded Operators IV ...
Contents
SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |
BAlgebras | 859 |
Commutative BAlgebras | 868 |
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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 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 prove real axis real numbers satisfies sequence solution spectral spectral theorem square-integrable subspace Suppose T₁ T₂ theory To(t topology transform unique unitary vanishes vector zero