## Linear Operators: Spectral theory |

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Page 1220

It is clear that G(S, 2, v) is a linear manifold in the space M(S, 2, v) of all v-

measurable functions on S and that a set of functions in G(S, 2, v) is

It is clear that G(S, 2, v) is a linear manifold in the space M(S, 2, v) of all v-

measurable functions on S and that a set of functions in G(S, 2, v) is

**linearly****independent**in M(S, 2, v) if and only if it is**linearly independent**in G(S, 2, v). The**linear**...Page 1306

The following table gives the number of

= 0 square integrable at a or b when J. (2) # 0. There are four possibilities as

shown by the discussion above. Number of

The following table gives the number of

**linearly independent**solutions of (r–2) a= 0 square integrable at a or b when J. (2) # 0. There are four possibilities as

shown by the discussion above. Number of

**linearly independent**solutions ...Page 1311

The operator T = T(t) will be an operator obtained from t by the imposition of a set,

which may be vacuous, of k

= 1,..., k; i.e., T is the restriction of Ti(t) (cf. Definition 2.8) to the submanifold of ...

The operator T = T(t) will be an operator obtained from t by the imposition of a set,

which may be vacuous, of k

**linearly independent**boundary conditions B, (f) = 0, i= 1,..., k; i.e., T is the restriction of Ti(t) (cf. Definition 2.8) to the submanifold of ...

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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