## Linear Operators: Spectral theory |

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scalar

chapter we shall only integrate bounded

discussion of the integral will be restricted to that case . Let Ebe a field of subsets

of a set S ...

scalar

**function**with respect to the operator valued set**function**E. In the presentchapter we shall only integrate bounded

**functions**f and so the followingdiscussion of the integral will be restricted to that case . Let Ebe a field of subsets

of a set S ...

Page 1178

It is plain from Plancherel's theorem that X is a bounded mapping of the space L ,

of scalar - valued

which maps the vector - valued

It is plain from Plancherel's theorem that X is a bounded mapping of the space L ,

of scalar - valued

**functions**into the space L2 ... Let M be the mapping in L ( 12 )which maps the vector - valued

**function**whose nth component has the Fourier ...Page 1922

Total space of functionals , definition , V.3.1 ( 418 ) Total variation of a

.5.15 ( 140 ) of a set

set , 1.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix

...

Total space of functionals , definition , V.3.1 ( 418 ) Total variation of a

**function**, III.5.15 ( 140 ) of a set

**function**, III.1.4 ( 97 ) . ( See also Variation ) Totally orderedset , 1.2.2 ( 4 ) Trace , of a finite matrix , VI.9.28 ( 515 ) , XI.6.8 ( 1016 ) of a matrix

...

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