## Linear Operators: Spectral theory |

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Page 966

For some choice off the integral on the right of [ * ] is not zero and since , by

Lemma 1 ( d ) , the integral on the left of [ * ] is

agrees almost everywhere with a

of ...

For some choice off the integral on the right of [ * ] is not zero and since , by

Lemma 1 ( d ) , the integral on the left of [ * ] is

**continuous**, we conclude that hmagrees almost everywhere with a

**continuous**function . By redefining him on a setof ...

Page 968

... is a topological group . PROOF . Verification that the neighborhoods N ( h , K ,

€ ) are a base for a topology will be left to the reader . If h , e N ( h , K , e ) and h ,

E N ( ho , K , 8 ) then hy h2 EN ( hho , K2 , ε ) so that multiplication is

... is a topological group . PROOF . Verification that the neighborhoods N ( h , K ,

€ ) are a base for a topology will be left to the reader . If h , e N ( h , K , e ) and h ,

E N ( ho , K , 8 ) then hy h2 EN ( hho , K2 , ε ) so that multiplication is

**continuous**.Page 1903

6 ( 428 ) criteria for existence of

- existence in Lp , 0 < p < 1 , V . 7 . 37 ( 438 )

Absolutely

6 ( 428 ) criteria for existence of

**continuous**linear functionals , V . 7 . 3 ( 436 ) non- existence in Lp , 0 < p < 1 , V . 7 . 37 ( 438 )

**Continuous**functions . ( See alsoAbsolutely

**continuous**functions ) as a B - space , additional properties , IV .### What people are saying - Write a review

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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