## Linear Operators: Self Adjoint Operators in Hilbert Space. Spectral theory. Part II |

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Page 1220

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

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

.

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

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

**linearly****independent**in M ( S , E , v ) if and only if it is**linearly independent**in G ( S , E , v ).

Page 1306

The following table gives the number of

a = 0 square integrable at a or b when .f(}.) ;é 0. There are four possibilities as

shown by the discussion above O Number of

The following table gives the number of

**linearly independent**solutions of (1: -1.)a = 0 square integrable at a or b when .f(}.) ;é 0. There are four possibilities as

shown by the discussion above O 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 T ( T ) ( cf. Definition 2.8 ) to the submanifold ...

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

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### Contents

SPECTRAL THEORY Self Adjoint Operators in Hilbert Space | 858 |

BAlgebras | 859 |

Preliminary Notions | 865 |

Copyright | |

61 other sections not shown

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### Common terms and phrases

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 Nauk neighborhood norm obtained partial positive preceding present problem projection proof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero