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

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Page 966

For some choice of | the integral on the right of [ * ] is not zero and since , by Lemma 1 ( d ) , the integral on the left of [ * ] is

For some choice of | the integral on the right of [ * ] is not zero and since , by Lemma 1 ( d ) , the integral on the left of [ * ] is

**continuous**, we conclude that hm agrees almost everywhere with a**continuous**function .Page 968

By IV.8.19 the integrable

By IV.8.19 the integrable

**continuous**functions on R are dense in Li ( R ) so there is a**continuous**function f on R such that fi < l and ( if ) ( mo ) + 0. Let a = ( tt ) ( mo ) so | ) , that 0 ) < a < 1 and let U be a neighborhood of m ...Page 1903

on non - existence in Ly , 0 ) < p < 1 , V.7.37 ( 438 )

on non - existence in Ly , 0 ) < p < 1 , V.7.37 ( 438 )

**Continuous**functions . ( See also Absolutely**continuous**functions ) as a B - space , additional properties , IV.15 definition , IV.2.14 ( 240 ) remarks concerning , ( 373-386 ) ...### 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