## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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Page 1147

COROLLARY : If G is a compact topological group satisfying the second axiom of countability , and G is not a

COROLLARY : If G is a compact topological group satisfying the second axiom of countability , and G is not a

**finite**set , then any complete set of representations of G is countable . A complete set of representations of a**finite**group ...Page 1908

... 1.7.10-12 ( 30–31 )

... 1.7.10-12 ( 30–31 )

**Finite**dimensional function Fréchet differential , definition , ( 92 ) theory for compact operators , VII.4 Fredholm alternative , ( 609-610 ) Fubini theorem , for general**finite**measure spaces , II1.11.13 ( 193 ) ...Page 1913

( See also Decomposition ) definition , III.4.3 ( 126 )

( See also Decomposition ) definition , III.4.3 ( 126 )

**finite**, III.4.3 ( 126 ) Lebesgue extension of , II1.5.18 ( 143 ) as a metric space , III.7.1 ( 158 ) , III.9.6 ( 169 ) positive , III.4.3 ( 126 ) product , of**finite**number of ...### What people are saying - Write a review

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additive adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined eigenvalues element equal equation Exercise exists extension fact finite dimensional follows formal formal differential operator formula function function f given Hence Hilbert space Hilbert-Schmidt ideal identity independent inequality integral interval isometric isomorphism Lemma limit linear matrix measure multiplicity neighborhood norm normal operator obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solution spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero