## Linear Operators, Part 2 |

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Page 1662

Then the closed set Cg in I , which is the complement of the largest open set in I

in which F vanishes , i . e . , which is the complement in I of the union of all the

open

Then the closed set Cg in I , which is the complement of the largest open set in I

in which F vanishes , i . e . , which is the complement in I of the union of all the

open

**subsets**of I in which F vanishes , is called the carrier of F . Lemma 12 now ...Page 1663

for each open

DEFINITION . Let I be an open

set of all F in D , ( I ) for which \ F ( q ) ) < co | Fli _ k ) = sup DEC 0 ( 1 ) 1911 ) will

...

for each open

**subset**1 . of I whose closure is compact and contained in I . 35DEFINITION . Let I be an open

**subset**of C and let k be a positive integer . ( i ) Theset of all F in D , ( I ) for which \ F ( q ) ) < co | Fli _ k ) = sup DEC 0 ( 1 ) 1911 ) will

...

Page 1696

By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has

a carrier which is a compact

Hence , we can evidently suppose without loss of generality that the carrier C of F

...

By Lemma 14 there is a sequence { Fm } of elements of D ( I ) , each of which has

a carrier which is a compact

**subset**C of I , and such that Fm → F as m → 00 .Hence , we can evidently suppose without loss of generality that the carrier C of F

...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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