## Linear Operators: Spectral theory |

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Page 1223

How are we to choose its

the collection or of all functions with one continuous derivative. If f and g are any

two such functions, we have (iDí, g) = | if'(t)q(t)at = | food Hi(f(1) (I)-f(0) (O) = (j, ...

How are we to choose its

**domain**? A natural first guess is to choose as**domain**the collection or of all functions with one continuous derivative. If f and g are any

two such functions, we have (iDí, g) = | if'(t)q(t)at = | food Hi(f(1) (I)-f(0) (O) = (j, ...

Page 1249

Thus PP" is a projection whose range is 92 = Post, the final

complete the proof it will suffice to show that P*P is a projection if P is a partial

isometry. Let w, vest, the initial

shows ...

Thus PP" is a projection whose range is 92 = Post, the final

**domain**of P. Tocomplete the proof it will suffice to show that P*P is a projection if P is a partial

isometry. Let w, vest, the initial

**domain**of P. Then the identity |x+v? = |Pr-i-Pus”shows ...

Page 1669

Nelson Dunford, Jacob T. Schwartz. The next topic on which we wish to touch is

that of the behavior of distributions under changes of variable. 44 DEFINITION.

Let II be a

II ...

Nelson Dunford, Jacob T. Schwartz. The next topic on which we wish to touch is

that of the behavior of distributions under changes of variable. 44 DEFINITION.

Let II be a

**domain**in E”, and let I, be a**domain**in E”. Let M : II – I, be a mapping ofII ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 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 Akad algebra Amer analytic applied assume Banach spaces basis belongs Borel boundary conditions boundary values bounded called clear closed closure coefficients compact complete 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 measure multiplicity neighborhood norm obtained partial positive preceding present problem projection PRoof properties prove range regular remark representation respectively restriction result satisfies seen sequence singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero