Linear Operators, Part 2 |
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Page 887
... tion theorem ( in particular Corollaries IX.3.9 and IX.3.15 ) will yield , for normal operators in Hilbert space , a reduction theory which is more complete than that developed in Chapter VII for general opera- tors in a complex B ...
... tion theorem ( in particular Corollaries IX.3.9 and IX.3.15 ) will yield , for normal operators in Hilbert space , a reduction theory which is more complete than that developed in Chapter VII for general opera- tors in a complex B ...
Page 1905
... tion , ( 318 ) equivalence with strong , IV.10 ( 318 ) Covering of a topological space , defi- nition , I.5.5 ( 17 ) Heine - Borel covering theorem , ( 17 ) Lindelöf covering theorem , ( 12 ) in the sense of Vitali , definition , III ...
... tion , ( 318 ) equivalence with strong , IV.10 ( 318 ) Covering of a topological space , defi- nition , I.5.5 ( 17 ) Heine - Borel covering theorem , ( 17 ) Lindelöf covering theorem , ( 12 ) in the sense of Vitali , definition , III ...
Page 1907
... tion , III.1.11 ( 100-101 ) Euclidean space , definition , IV.2.1 ( 238 ) further properties , IV.15 ( 374 ) study of , IV.3 Euler - Gauss , hypergeometric equa- tion of , XIII.8 ( 1509 ) Extended real and complex numbers , definitions ...
... tion , III.1.11 ( 100-101 ) Euclidean space , definition , IV.2.1 ( 238 ) further properties , IV.15 ( 374 ) study of , IV.3 Euler - Gauss , hypergeometric equa- tion of , XIII.8 ( 1509 ) Extended real and complex numbers , definitions ...
Contents
BAlgebras | 861 |
Commutative BAlgebras | 868 |
Commutative BAlgebras | 874 |
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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 coefficients compact operator complex numbers constant 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 subset subspace Suppose T₁ T₂ theory To(t topology unique unitary vanishes vector zero