## Linear Operators: Spectral theory |

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Page 942

Now if T, p = Aq, then J.g(su-)p(u)a(du) = *(s), seg, is a

replacing s by st and u by ut and using the fact that u(Et) = u(E) it is seen that s, g(

su-)p(u)a(du) = *(t), i.e., every translate p' of an eigenfunction p corresponding to

A ...

Now if T, p = Aq, then J.g(su-)p(u)a(du) = *(s), seg, is a

**continuous function**. Byreplacing s by st and u by ut and using the fact that u(Et) = u(E) it is seen that s, g(

su-)p(u)a(du) = *(t), i.e., every translate p' of an eigenfunction p corresponding to

A ...

Page 966

For some choice of f the integral on the right of [*] is not zero and since, by

Lemma 1 (d), the integral on the left of [*] is continuous, we conclude that h,

agrees almost everywhere with a

measure ...

For some choice of f the integral on the right of [*] is not zero and since, by

Lemma 1 (d), the integral on the left of [*] is continuous, we conclude that h,

agrees almost everywhere with a

**continuous function**. By redefining h, on a set ofmeasure ...

Page 1002

4 If f is a non-negative function in AP, and M(f) = 0 (in the notation of Exercise 2)

then f = 0. 5. A

almost periodic if for each e > 0 there exists a number L(e) such that each circle

in ...

4 If f is a non-negative function in AP, and M(f) = 0 (in the notation of Exercise 2)

then f = 0. 5. A

**continuous function**f of two real variables a = (a, ass) is calledalmost periodic if for each e > 0 there exists a number L(e) such that each circle

in ...

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### Contents

SPECTRAL THEORY | 858 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

34 other sections not shown

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