## Linear Operators: Spectral theory |

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Page 898

If we put E(0) = 0 when 6 no (T) is void, then

Theorem 1 and

spectral measure associated, in

If we put E(0) = 0 when 6 no (T) is void, then

**Corollary**4 follows immediately fromTheorem 1 and

**Corollary**IX.3.15. Q.E.D. 5 DEFINITION. The uniquely definedspectral measure associated, in

**Corollary**4, with the normal operator T is called ...Page 1301

However, as vo satisfies an equation of order 2n, vo must be identically zero. This

contradiction completes the proof. Q.E.D. 23

differential operator of order n on an interval I with end points a, b, and suppose

that the ...

However, as vo satisfies an equation of order 2n, vo must be identically zero. This

contradiction completes the proof. Q.E.D. 23

**CoRollary**. Let t be a formaldifferential operator of order n on an interval I with end points a, b, and suppose

that the ...

Page 1302

number of independent boundary values at a and at b respectively. The

statement of the present

) Under the ...

**Corollary**23 and from Theorems 19 and 20 that d' and d" exceed by n thenumber of independent boundary values at a and at b respectively. The

statement of the present

**corollary**is then evident. Q.E.D. 26**CoRollARY**. (Kodaira) Under the ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete Consequently constant contains continuous converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function function f given Hence Hilbert space identity independent indices inequality integral interval Lemma limit linear mapping Math measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero