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

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Page 995

Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set

Let h be in L ( R ) with himo ) = 1 and h vanishing on an open set

**containing**the remainder of off * ) . It follows from Lemma 12 that the set ( h * f * ° )**contains**at most the single point m , and hence , from Theorem 16 and Lemma 3.1 ...Page 996

From Lemma 12 ( b ) it is seen that b 018 * 9 ) Cola ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * 9 )

From Lemma 12 ( b ) it is seen that b 018 * 9 ) Cola ) and from Lemma 12 ( c ) and the equation of = Tf it follows that o ( f * 9 )

**contains**no interior point of o ( Q ) . Hence olf * 9 ) is a closed subset of the boundary of o ( q ) .Page 1456

Suppose for definiteness that I

Suppose for definiteness that I

**contains**a neighborhood of the left end point a of I , so that , unless I = I ( in which case T = 7 , and 1 is evidently bounded below ) , I ,**contains**a neighborhood of the right end point b of I. Unless ...### 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