Linear Operators: Spectral theory |
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Results 1-3 of 85
Page 1900
... properties , III.14 space of , definition , IV.2.24 ( 242 ) properties , IV.15 Annihilator of a set , II.4.17 ( 72 ) Arens ' lemma , IX.3.5 ( 875-876 ) Arzelà theorem , on continuity of limit function , IV.6.11 ( 268 ) remarks ...
... properties , III.14 space of , definition , IV.2.24 ( 242 ) properties , IV.15 Annihilator of a set , II.4.17 ( 72 ) Arens ' lemma , IX.3.5 ( 875-876 ) Arzelà theorem , on continuity of limit function , IV.6.11 ( 268 ) remarks ...
Page 1902
... properties , I.4.4–5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion to be in , 1.7.2 ( 27 ) definition , I.4.9 ( 11 ) properties of the closure operation , 1.4.10-11 ( 11-12 ) ...
... properties , I.4.4–5 ( 10 ) Closed sphere , II.4.1 ( 70 ) Closed unit sphere , II.3.1 ( 59 ) Closure of a set , criterion to be in , 1.7.2 ( 27 ) definition , I.4.9 ( 11 ) properties of the closure operation , 1.4.10-11 ( 11-12 ) ...
Page 1904
... properties , III.6.14–17 ( 150–151 ) in L ,, criteria for , III.3.6-7 ( 122– 124 ) , III.6.15 ( 150 ) , III.9.5 ... properties , III.2.7-8 ( 104-105 ) , III.6.2-3 ( 145 ) , III.6.13 ( 150 ) quasi - uniform , definition , IV.6.10 ( 268 ) ...
... properties , III.6.14–17 ( 150–151 ) in L ,, criteria for , III.3.6-7 ( 122– 124 ) , III.6.15 ( 150 ) , III.9.5 ... properties , III.2.7-8 ( 104-105 ) , III.6.2-3 ( 145 ) , III.6.13 ( 150 ) quasi - uniform , definition , IV.6.10 ( 268 ) ...
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