## Linear Operators: Spectral theory |

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Page 942

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. ing to an

eigenvalue A A 0 form a finite dimensional space. Now if T,p = Ap then J. g(suT")

p(u)u(du) = Asp(s), s e G, is a

ut ...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. ing to an

eigenvalue A A 0 form a finite dimensional space. Now if T,p = Ap then J. g(suT")

p(u)u(du) = Asp(s), s e G, is a

**continuous function**. By replacing s by st and u byut ...

Page 966

For some choice of f the integral on the right of [+] is not zero and since, by

Lemma 1 (d), the integral on the left of [*] is continuous, we conclude that h,

agrees almost everywhere with a

measure ...

For some choice of f the integral on the right of [+] is not zero and since, by

Lemma 1 (d), the integral on the left of [*] is continuous, we conclude that h,

agrees almost everywhere with a

**continuous function**. By redefining h, on a set ofmeasure ...

Page 1002

4 If f is a non-negative function in AP, and M(f) = 0 (in the notation of Exercise 2)

then f = 0. 5 A

almost periodic if for each e > 0 there exists a number L(e) such that each circle

in ...

4 If f is a non-negative function in AP, and M(f) = 0 (in the notation of Exercise 2)

then f = 0. 5 A

**continuous function**f of two real variables a = (a 1, ag) is calledalmost periodic if for each e > 0 there exists a number L(e) such that each circle

in ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

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

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero