## Linear Operators: Spectral theory |

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Page 1074

is the

transform of a function in L.,(– co, + oc), the

in Exercise 6. 10 Let à be a function defined on (– 00, + 00) which is of finite total

...

is the

**Fourier**transform of a function in L.,(–oo, -i- oc) whenever F is the**Fourier**transform of a function in L.,(– co, + oc), the

**Fourier**transforms being defined asin Exercise 6. 10 Let à be a function defined on (– 00, + 00) which is of finite total

...

Page 1075

F(t)e-* dt, - 27 J_A F denoting the

inequality Sup ... A > 0 16 Show that not every continuous function, defined for –

o – t < 00 and approaching zero as t approaches + o or — o, is the

transform of a ...

F(t)e-* dt, - 27 J_A F denoting the

**Fourier**transform of f, fails to satisfy theinequality Sup ... A > 0 16 Show that not every continuous function, defined for –

o – t < 00 and approaching zero as t approaches + o or — o, is the

**Fourier**transform of a ...

Page 1176

Let p, q, k, be as in the preceding lemma, and, for each N, let X^N be the

transformation in L,(l,) which maps the vector whose nth component has the

transform k,($)f ...

Let p, q, k, be as in the preceding lemma, and, for each N, let X^N be the

transformation in L,(l,) which maps the vector whose nth component has the

**Fourier**transform f,($) into the vector whose nth component has the**Fourier**transform k,($)f ...

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

Copyright | |

48 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 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