## Linear Operators: Spectral theory |

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Page 1145

4 is basic to the theory of

definitions and theorems of this theory are as follows . DEFINITION : Let G be a

topological group , and X a B - space . Then a

strongly ...

4 is basic to the theory of

**representations**of compact groups . The principaldefinitions and theorems of this theory are as follows . DEFINITION : Let G be a

topological group , and X a B - space . Then a

**representation**R of G in X is astrongly ...

Page 1146

Any finite dimensional

irreducible

dimensional

generality ...

Any finite dimensional

**representation**of a compact group G is a direct sum ofirreducible

**representations**. This theorem shows that in studying finitedimensional

**representations**of a compact group G we may , without loss ofgenerality ...

Page 1217

A spectral

adjoint operator T in v is said to be an ordered

The measure u is called the measure of the ordered

...

A spectral

**representation**of a Hilbert space H onto En L2 ( Mn ) relative to a selfadjoint operator T in v is said to be an ordered

**representation**of H relative to T .The measure u is called the measure of the ordered

**representation**. The sets en...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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additive adjoint operator 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 shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero