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

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Finally we show that the decomposition T = PA of the theorem is

Finally we show that the decomposition T = PA of the theorem is

**unique**. ... Since A is**unique**, P is**uniquely**determined on R ( A ) by the equation of P ( Ax ) = Tx . Further the extension of P by continuity from R ( A ) to R ( A ) is ...Page 1283

Thus , equation ( e ' ) has the

Thus , equation ( e ' ) has the

**unique**solution ( cf. Lemma VII.3.4 ) F = ( 1 + 0 ) -H = E ( -1 ) ; ØH . o j = 0 Since all the terms in equation ( e ) but the first are absolutely continuous , it follows that F is absolutely continuous ...Page 1383

With boundary conditions A and C , the

With boundary conditions A and C , the

**unique**solution of tzo = lo satisfying the boundary condition 720 = lo is sin vīt . With boundary conditions A , the eigenvalues are consequently to be determined from the equation sin vã = 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 |

### 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