## Linear Operators: Spectral theory |

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Page 972

From the preceding lemma it is seen that (tT"X.1,)(a) = [a, p]t'T'z., a e R. Since

characters have modulus

argument just given to conclude that Au(e) = u(e–H p-p) < 00 and

).

From the preceding lemma it is seen that (tT"X.1,)(a) = [a, p]t'T'z., a e R. Since

characters have modulus

**equal**to unity, ... e and p by e-Hp and —p in theargument just given to conclude that Au(e) = u(e–H p-p) < 00 and

**equals**u(e–H p).

Page 1147

(b) Any irreducible representation of G is

R*). ... the number of representations in a complete set of representations is

(b) Any irreducible representation of G is

**equivalent**to one of the representationsR*). ... the number of representations in a complete set of representations is

**equal**to the number of distinct classes of G. The main aim of the representation ...Page 1539

Then the point % belongs to the essential spectrum of t. A6 Let t be a regular

formally symmetric formal differential operator on [0, oo) with

indices, and let A be a real number. Prove that the distance from 2 to the

essential ...

Then the point % belongs to the essential spectrum of t. A6 Let t be a regular

formally symmetric formal differential operator on [0, oo) with

**equal**deficiencyindices, and let A be a real number. Prove that the distance from 2 to the

essential ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 other sections not shown

### 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