## Linear Operators: Spectral operators |

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Page 2051

We next

Cauchy problem whose existence is established in Theorem 19 . As before , we

assume that aét > 0 . It follows from equation ( 55 ) which gives the analytical ...

We next

**consider**the problem of finding the explicit form of the solu . tion to theCauchy problem whose existence is established in Theorem 19 . As before , we

assume that aét > 0 . It follows from equation ( 55 ) which gives the analytical ...

Page 2486

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 14 Let H

be a Hilbert space , R the real axis , and

H be the self adjoint operator in L , defined by ( Hf ) ( x ) = xf ( x ) . For each pe L2

...

Nelson Dunford, Jacob T. Schwartz, William G. Bade, Robert G. Bartle. 14 Let H

be a Hilbert space , R the real axis , and

**consider**the space L2 = L2 ( R , H ) . LetH be the self adjoint operator in L , defined by ( Hf ) ( x ) = xf ( x ) . For each pe L2

...

Page 2488

J - 00 ( Hint :

( a ) Let f be a continuous function of bounded variation on an interval [ a , b ] ,

and let V ( f ) denote its total variation . Show that set = f ( x ) dx < 2 max \ f ( x ) ] +

V ...

J - 00 ( Hint :

**Consider**A self adjoint , and expand in the eigenvectors of A . ) . 17( a ) Let f be a continuous function of bounded variation on an interval [ a , b ] ,

and let V ( f ) denote its total variation . Show that set = f ( x ) dx < 2 max \ f ( x ) ] +

V ...

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