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

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Page 1074

8 Show , with the hypotheses and notation of Exercise 6 , that if b is in Lol - 00 , +00 ) , then Ste 16 ( ) 2-- | F ( t ) / P dt < c . 9 Let 2 be a real function of a real variable such that 1. F. ) is the Fourier

8 Show , with the hypotheses and notation of Exercise 6 , that if b is in Lol - 00 , +00 ) , then Ste 16 ( ) 2-- | F ( t ) / P dt < c . 9 Let 2 be a real function of a real variable such that 1. F. ) is the Fourier

**transform**of a ...Page 1075

15 Show that there exists a function f in Lil - 00 , + ) for which the family of functions a 1 ta ( x ) s F ( t ) e - ita dt , 27 A F denoting the Fourier

15 Show that there exists a function f in Lil - 00 , + ) for which the family of functions a 1 ta ( x ) s F ( t ) e - ita dt , 27 A F denoting the Fourier

**transform**of f , fails to satisfy the inequality sup A > 0 sta ( r ) dx < 0 .Page 1271

frequently - used device , it is appropriate that we give a brief sketch indicating how the Cayley

frequently - used device , it is appropriate that we give a brief sketch indicating how the Cayley

**transform**can be used to determine when a symmetric operator has a self adjoint extension . Let T be a symmetric operator with domain D ...### 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