## Linear operators: Spectral operators |

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Page 1983

that the measure spaces (RN, 2, ds) and (S, Z, ds) are the same. The algebra (t

consists of all d which are continuous on S, that is, all continuous complex ...

**Lebesgue**measure is extended to S by letting the set {oo} have measure zero sothat the measure spaces (RN, 2, ds) and (S, Z, ds) are the same. The algebra (t

consists of all d which are continuous on S, that is, all continuous complex ...

Page 1998

Since f <ptK(dt)= f ftfMdt, •>bn jrn it follows from 111.11.17 that (An * <p)(a) = f <p(

s- t)fn(t) dt = f fn(s - t)<p(t) dt, JrN JrH and that the integral exists in the sense of

8.

Since f <ptK(dt)= f ftfMdt, •>bn jrn it follows from 111.11.17 that (An * <p)(a) = f <p(

s- t)fn(t) dt = f fn(s - t)<p(t) dt, JrN JrH and that the integral exists in the sense of

**Lebesgue**for almost all s in RN. The corollary thus follows from Theorems 5 and8.

Page 2410

Let A(z, z') be a

the sjmce B(X) of all bounded operators in X. Suppose that (35) \\A || = sup \A(z, z'

)\ < oo, 2,2'eD and let <p(A) be the integral operator defined by the equation (36)

...

Let A(z, z') be a

**Lebesgue**measurable function defined in D x D, with values inthe sjmce B(X) of all bounded operators in X. Suppose that (35) \\A || = sup \A(z, z'

)\ < oo, 2,2'eD and let <p(A) be the integral operator defined by the equation (36)

...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

47 other sections not shown

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