## Linear Operators: Spectral theory |

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Page 945

In

In

**fact**, the theory will be applied in this section to prove the principal result in H. Bohr's theory of almost periodic functions . It has been observed ( IV.7.6 ) that there is a compact Hausdorff space S such that AP is ...Page 1245

This result may be regarded as a far - reaching generalization of the

This result may be regarded as a far - reaching generalization of the

**fact**that each complex number « has a unique representation & = reil , where r 20 , and lei ) = 1. By analogy with the**fact**that r = ( ão ) , , we shall first seek to ...Page 1348

are in

are in

**fact**entire in 2. In the range a > 0 they form a perfectly suitable basis for the solutions of to ho . However , in the range 2 < 0,14 is imaginary , and an analytic expression like cos att is hard to work with because of the ...### What people are saying - Write a review

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### Contents

8 | 876 |

859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

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### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume basis belongs Borel set boundary conditions boundary values bounded called clear closed closure commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues elements equal equation equivalent Exercise exists extension fact finite dimensional follows follows from Lemma formal differential operator formula function given Hence Hilbert space Hilbert-Schmidt ideal identity immediately implies independent inequality integral interval invariant isometric isomorphism Lemma limit linear Ly(R mapping matrix measure multiplicity neighborhood norm obtained orthonormal positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown shows solutions spectral spectrum square-integrable statement subset subspace sufficient Suppose symmetric Theorem theory topology transform uniformly unique unit unitary vanishes vector zero