## Linear Operators: Spectral theory |

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Page 963

Nelson Dunford, Jacob T. Schwartz.

multiplying the corresponding function tf in L ( M ) by the characteristic function of

the set e . Similarly , convolution in L ( R ) corresponds to pointwise multiplication

...

Nelson Dunford, Jacob T. Schwartz.

**unique**exten asion is dentro L2 ( Mo , B tomultiplying the corresponding function tf in L ( M ) by the characteristic function of

the set e . Similarly , convolution in L ( R ) corresponds to pointwise multiplication

...

Page 1250

Finally we show that the decomposition T = PA of the theorem is

A is

Further the extension of P by continuity from R ( A ) to R ( A ) is

Finally we show that the decomposition T = PA of the theorem is

**unique**. ... SinceA is

**unique**, P is**uniquely**determined on R ( A ) by the equation of P ( Ax ) = Tx .Further the extension of P by continuity from R ( A ) to R ( A ) is

**unique**. Since P ...Page 1513

Let Ft be the

and exponents which has the form 2 - 2 ( 1 + x + . . . ) near z = 0 . Then , since F ,

and Ft together comprise a basis for the solutions of our equation , we have a ...

Let Ft be the

**unique**solution of the equation with these same regular singularitiesand exponents which has the form 2 - 2 ( 1 + x + . . . ) near z = 0 . Then , since F ,

and Ft together comprise a basis for the solutions of our equation , we have a ...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 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 Akad 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 Russian satisfies seen sequence shown singular solution spectral square-integrable statement subset subspace sufficiently Suppose symmetric Theorem theory topology transform unique vanishes vector zero