## Linear operators. 2. Spectral theory : self adjoint operators in Hilbert Space |

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... i.e. , with all the maximal ideals of the algebra

... i.e. , with all the maximal ideals of the algebra

**obtained**by adjoining an identity to L ( R ) except the point at infinity of M. Now in an algebra with identity every ideal is contained in a maximal ideal , but if an identity is ...Page 1318

for di Suppose that the homogeneous system

for di Suppose that the homogeneous system

**obtained**from equations [ 1 ' ] and [ 2 ' ] has a non - trivial solution a ? ( c ) , B ( c ) , and let K. ( - ) be the function ( of the variable s )**obtained**by substituting and po and Bi in ...Page 1624

In the same way , the functions cos tvā

In the same way , the functions cos tvā

**obtained**from the operator to enjoy the property so cos svā cos tvāu ( da ) ... Their first step consists in**obtaining**an expression for f ( t , 2 ) as a “ linear combination ” of the functions cos ...### 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 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

Linear Operators, Part 2: Spectral Theory, Self Adjoint Operators in Hilbert ... Nelson Dunford,Jacob T. Schwartz No preview available - 1988 |

### Common terms and phrases

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