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

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Page 1064

( 1 ) - = | 2 ( u ) f ( x - u ) du \ u121 \ u / "

( 1 ) - = | 2 ( u ) f ( x - u ) du \ u121 \ u / "

**satisfies**the inequality g1 S14,1 , where I Ss 12 ( w ) \ u ( do ) . To do this , let { 2m } be a sequence of odd functions , each infinitely often differentiable in the neighborhood of ...Page 1460

By Theorem XII.2.6 , every function f in E L ,

By Theorem XII.2.6 , every function f in E L ,

**satisfies**Tf = hif . Since by Theorem 2.10 and Lemma XII.4.1 ( b ) , Tj = his implies Ti ( t ) t = hit , it follows that E ( L2 ( 1 ) ) is finite dimensional for each i = 1 , ... , p .Page 1602

( 48 ) Suppose that the function q is bounded below , and let i be a real solution of the equation ( 2-1 ) } = 0 on [ 0 , 0 ) which is not square - integrable but which

( 48 ) Suppose that the function q is bounded below , and let i be a real solution of the equation ( 2-1 ) } = 0 on [ 0 , 0 ) which is not square - integrable but which

**satisfies**S 1 ( ) ] ? ds = 0 ( tk ) for some k > 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