## Linear Operators: Spectral theory |

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Page 1147

( b ) Any irreducible representation of G is

representations R ( « ) . ... in a complete set of representations is

number of distinct classes of G . The main aim of the representation theory of

compact groups is to ...

( b ) Any irreducible representation of G is

**equivalent**to one of therepresentations R ( « ) . ... in a complete set of representations is

**equal**to thenumber of distinct classes of G . The main aim of the representation theory of

compact groups is to ...

Page 1396

Then both deficiency indices of t are

extensions of Tolt ) have the same set of non - isolated points , and this set is

5 and ...

Then both deficiency indices of t are

**equal**. Moreover , all the self adjointextensions of Tolt ) have the same set of non - isolated points , and this set is

**equal**to oclt ) . PROOF . The second assertion follows immediately from Theorem5 and ...

Page 1539

A6 Let T be a regular formally symmetric formal differential operator on [ 0 , 00 )

with

distance from 2 to the essential spectrum of 1 is less than or

if there ...

A6 Let T be a regular formally symmetric formal differential operator on [ 0 , 00 )

with

**equal**deficiency indices , and let à be a real number . Prove that thedistance from 2 to the essential spectrum of 1 is less than or

**equal**to K if and onlyif there ...

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### Contents

IX | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

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 consider 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 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