## Linear Operators: Spectral theory |

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Page 1036

Then the λα , infinite product λ , Pi ( T ) a ů ( 2- ) i = elila i = 1

Then the λα , infinite product λ , Pi ( T ) a ů ( 2- ) i = elila i = 1

**converges**and defines a function analytic for 2 # 0 . For each fixed 1 + 0 , P. ( T ) is a continuous complex valued function on the B - space of all Hilbert ...Page 1436

Let { 8n } be a bounded sequence of elements of D ( T ) such that { Tgn }

Let { 8n } be a bounded sequence of elements of D ( T ) such that { Tgn }

**converges**. Find a subsequence { gn ; } { h ; } such that x * ( h ; )**converges**for each j , 1 si Sk . Then ħ ; = h ; - } _ 12 * ( hi ) p , is in D , and Thi ...Page 1664

The Fourier series of an element F in D , ( C )

The Fourier series of an element F in D , ( C )

**converges**unconditionally to F. PROOF . It follows from the Definition 37 of the topology in D , ( C ) that it suffices to show that ( 27 ) - " ? F ΣΕ . ) . eil . p ( x ) dx**converges**...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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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 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