## Linear Operators: Spectral theory |

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Page 963

tf in L ( M ) by the characteristic function of the set e . Similarly , convolution in L (

R ) corresponds to pointwise multiplication in L2 ( M . ) . 9 THEOREM .

**unique**exten asion is dentro L2 ( Mo , B to multiplying the corresponding functiontf in L ( M ) by the characteristic function of the set e . Similarly , convolution in L (

R ) corresponds to pointwise multiplication in L2 ( M . ) . 9 THEOREM .

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 | |

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