## Linear Operators: Spectral theory |

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Results 1-3 of 83

Page 973

t mapping

e) = A(t(e)), e e B, where 3 is the family of Borel sets

measure

t mapping

**R**onto all**of R**with the properties [**r**, m) = e^*(*), a e**R**, m e**R**and 2:tu(e) = A(t(e)), e e B, where 3 is the family of Borel sets

**in R**and where 2 is Haarmeasure

**on R**. PRoof. For a fixed m in .40 =**R**, the character sa, m), a e**R**, is a ...Page 1291

... compact subset may vary with the function). 8 DEFINITION. If t is a (regular or

irregular) differential operator of order n, we define the operators

L2(I) by the formulas (a) os

... compact subset may vary with the function). 8 DEFINITION. If t is a (regular or

irregular) differential operator of order n, we define the operators

**To(r**) and Ti(t) inL2(I) by the formulas (a) os

**To(r**)) = H(I), To(t)f = rs, fe?(**To(r**)), (b) Q(TA(**r**)) = H'(I), ...Page 1437

Suppose that a bounded sequence {fi} of elements of 3 (

–70)f,} converges but the sequence {f,} has no convergent subsequence. Then,

since

Suppose that a bounded sequence {fi} of elements of 3 (

**To(r**)) exists such that {(t–70)f,} converges but the sequence {f,} has no convergent subsequence. Then,

since

**To(r**) C Ti(t), it follows immediately from the preceding lemma that Zoe g ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

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### Other editions - View all

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