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

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Page 1218

... there is a Borel set o in R with u ( c ) < and such that the

... there is a Borel set o in R with u ( c ) < and such that the

**restriction**of 1 to the complement of o is continuous . Proof . If the**restrictions**flo , gd are continuous then so is the**restriction**( af + Bg ) o n d and thus the class ...Page 1239

Conversely , let T , be a self adjoint extension of T. Then by Lemma 26 , T is the

Conversely , let T , be a self adjoint extension of T. Then by Lemma 26 , T is the

**restriction**of T * to a subspace W of D ( T * ) determined by a symmetric family of linearly independent boundary conditions B1 ( x ) = 0 , i = 1 , ...Page 1471

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self adjoint

By Theorem 2.30 and Corollary 2.31 , a set of boundary conditions defining a self adjoint

**restriction**T of T1 ( T ) is of the form B ( / ) = QG ( ) + 62G2 ( / ) = 0 , až + až 70 , B ( f ) = B , G ( 1 ) + B2G2 ( t ) = 0 , Bi + B3 +0 ...### 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