## Linear Operators: Spectral theory |

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Page 972

... that ( T ? Ke + p ) ( x ) = { x , p ] T- \ kes 2 6 R. Since characters have modulus

Hence if ule ) < oo , we have proved that use + p ) is also finite and

... that ( T ? Ke + p ) ( x ) = { x , p ] T- \ kes 2 6 R. Since characters have modulus

**equal**to unity , it follows from Plancherel's theorem that { u ( e + p ) } 2 = { u ( e ) }Hence if ule ) < oo , we have proved that use + p ) is also finite and

**equals**ule ) .Page 1147

( b ) Any irreducible representation of G is

representations Rķa ) . ... complete set of representations is

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

groups is to display ...

( b ) Any irreducible representation of G is

**equivalent**to one of therepresentations Rķa ) . ... complete set of representations is

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

groups is to display ...

Page 1396

Then both deficiency indices of t are

extensions of To ( t ) have the same set of non - isolated points , and this set is

and ...

Then both deficiency indices of t are

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

**equal**to 0 ( t ) . Proof . The second assertion follows immediately from Theorem 5and ...

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Copyright | |

57 other sections not shown

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