## Linear Operators: Spectral theory |

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Page 909

The proof follows immediately , for since L SM , we have ( Lx , x ) < ( Mx , x ) for

every æ in H . Hence the characterization of an , Men

that an Ellion for all n = 1 , 2 , . . . . 5 . Spectral Representation Let u be a finite ...

The proof follows immediately , for since L SM , we have ( Lx , x ) < ( Mx , x ) for

every æ in H . Hence the characterization of an , Men

**given**in Theorem 3 showsthat an Ellion for all n = 1 , 2 , . . . . 5 . Spectral Representation Let u be a finite ...

Page 1149

likewise

representations , which , if one tries to regard them as representations of the

rotation group itself , turn out to be doublevalued . These representations are the

so ...

likewise

**given**by irreducible sets of tensors . The group RÙ ( n ) has additionalrepresentations , which , if one tries to regard them as representations of the

rotation group itself , turn out to be doublevalued . These representations are the

so ...

Page 1273

The simplification ,

presented in the text . ... Krein [ 9 ] has made a systematic study of all the

extensions of a semi - bounded operator , and also

differential ...

The simplification ,

**given**by Freudenthal [ 3 ] , of Friedrichs ' proof is the onepresented in the text . ... Krein [ 9 ] has made a systematic study of all the

extensions of a semi - bounded operator , and also

**given**applications todifferential ...

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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