## Linear Operators: Spectral theory |

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Page 884

In their proof , they

was not generally available . The proof of this ... A simple direct proof of Corollary

3.6 was given by Fukamiya [ 2 ] , and can be used to

...

In their proof , they

**proved**Lemma 3.5 by using a fairly deep result of Šilov thatwas not generally available . The proof of this ... A simple direct proof of Corollary

3.6 was given by Fukamiya [ 2 ] , and can be used to

**prove**Lemma 3.5 . Corollary...

Page 964

Using the portion of ( a ) already

82 ) = S. ( 18 ) ( m ) ( tg ) ( m ) _ ( dm ) . Since this identity ... Once it has been

shown that r 1 is everywhere defined on Mo , this will

remains ...

Using the portion of ( a ) already

**proved**, we obtain ( TE ( e ) g , rgı ) ( E ( e ) g ,82 ) = S. ( 18 ) ( m ) ( tg ) ( m ) _ ( dm ) . Since this identity ... Once it has been

shown that r 1 is everywhere defined on Mo , this will

**prove**part ( b ) . All thatremains ...

Page 1133

Q.E.D. We have also

operator of the operator Kof the preceding lemma is defined by the set K , of

kernels defined by K * ( s , t ) Kji ( t , 8 ) . The following theorem gives the ...

Q.E.D. We have also

**proved**the following corollary . 6 COROLLARY . The adjointoperator of the operator Kof the preceding lemma is defined by the set K , of

kernels defined by K * ( s , t ) Kji ( t , 8 ) . The following theorem gives the ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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additive Akad 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 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 matrix measure multiplicity neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result Russian satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero