## Linear Operators: Spectral theory |

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Page 894

The integral s f ( s ) E ( ds nd ) is itself a bounded additive set function for 8 in E ,

and thus the integral of a function g in B ( S , E ) with respect to this set function is

written as Søg ( t ) [ $ t ( s ) E ( ds o dt ) . If f is the characteristic

The integral s f ( s ) E ( ds nd ) is itself a bounded additive set function for 8 in E ,

and thus the integral of a function g in B ( S , E ) with respect to this set function is

written as Søg ( t ) [ $ t ( s ) E ( ds o dt ) . If f is the characteristic

**function of**a set ...Page 951

To begin the study , some basic properties of convolutions will be obtained . 1

LEMMA . ( a ) If f is a - measurable , then the

measurable function . ( b ) For f , geL ( R ) the

integrable in y for ...

To begin the study , some basic properties of convolutions will be obtained . 1

LEMMA . ( a ) If f is a - measurable , then the

**function f**( x − y ) is a 2 x 2 -measurable function . ( b ) For f , geL ( R ) the

**function f**( x − y ) g ( y ) isintegrable in y for ...

Page 1075

14 Show that there exists a continuous functions in L ( - 00 , toon L2 ( - 0 , + 00 )

such that the limit in Exercise 12 fails to exist for x = 0 . 15 Show that there exists

a

...

14 Show that there exists a continuous functions in L ( - 00 , toon L2 ( - 0 , + 00 )

such that the limit in Exercise 12 fails to exist for x = 0 . 15 Show that there exists

a

**function f**in L ( - 00 , + 00 ) for which the family of functions 1 p + A f ( x ) = - T F...

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### Contents

IX | 859 |

Eigenvalues and Eigenvectors | 903 |

Spectral Representation | 911 |

Copyright | |

15 other sections not shown

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