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

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Page 890

2x } of T and otherwise let E ( d ) be the sum of all the projections E ( 2 ) ... One class of scalar

2x } of T and otherwise let E ( d ) be the sum of all the projections E ( 2 ) ... One class of scalar

**functions f**, other than polynomials , for which the ...Page 986

Linear combinations of the translates of a

Linear combinations of the translates of a

**function f**in L ( R ) are dense in L ( R ) if and only if its transform f does not vanish on the character group ...Page 1075

if f is of bounded variation in the neighborhood of x . ... 14 Show that there exists continuous

if f is of bounded variation in the neighborhood of x . ... 14 Show that there exists continuous

**function f**in L ( -00 , +00 ) L ( -0 , +00 ) such that the ...### What people are saying - Write a review

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

37 other sections not shown

### 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