## Linear Operators: Spectral theory |

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Page 1343

Thus E(M(A); U) is non-zero for A near Ao, Že oo, and it follows that for A

of distinct points in the spectrum of M(A), the sets {2 e ooln(A) > s? are relatively

open in ...

Thus E(M(A); U) is non-zero for A near Ao, Že oo, and it follows that for A

**sufficiently**close to Ao, a (M(A)) n U is non-void. Thus if n(A) denotes the numberof distinct points in the spectrum of M(A), the sets {2 e ooln(A) > s? are relatively

open in ...

Page 1449

Nelson Dunford, Jacob T. Schwartz. for ao

do for ao

decreasing for

Nelson Dunford, Jacob T. Schwartz. for ao

**sufficiently**large, and if. s. q(t)|-*dt « oodo for ao

**sufficiently**large, then o,(r) is void. (d) If q(t) → —oo, if q is monotonedecreasing for

**sufficiently**...Page 1450

Nelson Dunford, Jacob T. Schwartz. q'(t) , (q(t)')* bo r s (#) –4.jä" so for

small bo, and if bo s q(t)|-*dt - o o for

(t) → — o as t → 0, q(t) is monotone decreasing for

...

Nelson Dunford, Jacob T. Schwartz. q'(t) , (q(t)')* bo r s (#) –4.jä" so for

**sufficiently**small bo, and if bo s q(t)|-*dt - o o for

**sufficiently**small bo, then o',(t) is void. (d) If q(t) → — o as t → 0, q(t) is monotone decreasing for

**sufficiently**small t, so ( q'(t) )-;...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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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