## Linear Operators: Spectral theory |

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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 too ft 16 ( t ) | 2 - P F ( t ) | ” dt < 0 . 9 Let 2 be a real function of a real

variable such that 1 ( • ) F ( 0 ) is the Fourier

00 ) ...

8 Show , with the hypotheses and notation of Exercise 6 , that if b is in Lol - 00 , +

00 ) , then too ft 16 ( t ) | 2 - P F ( t ) | ” dt < 0 . 9 Let 2 be a real function of a real

variable such that 1 ( • ) F ( 0 ) is the Fourier

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

Page 1075

... + 00 ) for which the family of functions p + A fa ( x ) = | F ( t ) e - ita dt , 27 J - A F

denoting the Fourier

approaching zero as t approaches too or - 00 , is the Fourier

function f in L ...

... + 00 ) for which the family of functions p + A fa ( x ) = | F ( t ) e - ita dt , 27 J - A F

denoting the Fourier

**transform**of f , fails to ... defined for - 00 < t < oo andapproaching zero as t approaches too or - 00 , is the Fourier

**transform**of afunction f in L ...

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 |

Bounded Normal Operators in Hilbert Space | 887 |

Compact Groups | 945 |

Copyright | |

46 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 operator algebra Amer analytic assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complex Consequently consider constant contains continuous converges Corollary corresponding defined Definition denote dense derivatives determined domain eigenvalues element equal equation essential spectrum evident Exercise exists extension finite follows formal differential operator formula function 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