## Linear Operators: Spectral theory |

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By elementary arguments such as those employed in the third paragraph of the proof of Lemma 6 , which we leave to the reader to elaborate in detail , we may conclude that to establish ( a ) in general it is sufficient to

By elementary arguments such as those employed in the third paragraph of the proof of Lemma 6 , which we leave to the reader to elaborate in detail , we may conclude that to establish ( a ) in general it is sufficient to

**consider**the ...Page 1155

We now

We now

**consider**the special form that the results of Sections 3 and 4 take when R is a compact Abelian group , a case studied explicitly in Section 1 . 8 THEOREM . If R is a compact Abelian group , its character group Ř is discrete .Page 1305

We conclude this section by

We conclude this section by

**considering**some simple examples of differential operators . The simplest example of a formally ... We shall**consider**three choices for the interval I. Case 1 : I = 0,1 ] . Here clearly d = [ = d_ = d = 1 ...### What people are saying - Write a review

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### Contents

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859 | 885 |

extensive presentation of applications of the spectral theorem | 911 |

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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