## Linear Operators: Spectral theory |

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Page 1074

19 . ) 8 Show , with the hypotheses and notation of Exercise 6 , that if b is in L , 1 -

0 , + 00 ) , then b ( t ) / 2 - P | F ( t ) | ” dt < 0 . 9 Let 2 be a real function of a real

variable such that 2 ( • ) F ( - ) is the Fourier

00 ) ...

19 . ) 8 Show , with the hypotheses and notation of Exercise 6 , that if b is in L , 1 -

0 , + 00 ) , then b ( t ) / 2 - P | F ( t ) | ” dt < 0 . 9 Let 2 be a real function of a real

variable such that 2 ( • ) F ( - ) is the Fourier

**transform**of a function in L , ( - 00 , +00 ) ...

Page 1075

15 Show that there exists a functions in Li ( - 00 , + 00 ) for which the family of

functions tn 1 gta † A ( x ) = = F ( t ) e - ite dt , 20 J - A F denoting the Fourier

that not ...

15 Show that there exists a functions in Li ( - 00 , + 00 ) for which the family of

functions tn 1 gta † A ( x ) = = F ( t ) e - ite dt , 20 J - A F denoting the Fourier

**transform**of f , fails to satisfy the inequality sup \ / ( x ) \ dx < 00 . A > OJ 16 Showthat not ...

Page 1271

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

how the Cayley

has a self adjoint extension . Let T be a symmetric operator with domain D ( T ) ...

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 operatorhas a self adjoint extension . Let T be a symmetric operator with domain D ( T ) ...

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### Contents

IX | 859 |

extensive presentation of applications of the spectral theorem | 911 |

Miscellaneous Applications | 937 |

Copyright | |

20 other sections not shown

### Other editions - View all

Linear Operators, Part 1 Nelson Dunford,Jacob T. Schwartz,William G. Bade,Robert G. Bartle Snippet view - 1958 |

### Common terms and phrases

additive adjoint adjoint operator algebra analytic assume B-algebra basis belongs Borel set boundary conditions boundary values bounded called clear closed closure coefficients commutative compact complex Consequently consider constant contains converges Corollary corresponding defined Definition denote dense determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension fact finite follows formal differential operator formula function function f give given Hence Hilbert space ideal identity independent indices inequality integral interval isometric isomorphism Lemma linear mapping matrix measure multiplicity neighborhood norm normal operator obtained positive preceding present projection proof properties prove range regular representation respectively restriction result satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique unit vanishes vector zero