## Linear Operators, Part 2 |

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Page 970

In this notation the formula in Theorem 11 becomes ( vf ) ( m ) = Sa [ x , m ] f ( x )

dx , fe Ly ( R ) , me Mo In Theorem 9 the domain of t was extended to L2 ( R ) ; we

wish to obtain a

In this notation the formula in Theorem 11 becomes ( vf ) ( m ) = Sa [ x , m ] f ( x )

dx , fe Ly ( R ) , me Mo In Theorem 9 the domain of t was extended to L2 ( R ) ; we

wish to obtain a

**similar**integral representation for this extension . Let & be the ...Page 1250

The Hamburger moment problem is

using the whole real axis ( -00 , 00 ) instead of [ 0 , 00 ) . The Hausdorff moment

problem is again

The Hamburger moment problem is

**similar**to that of Stieltjes and differs from it byusing the whole real axis ( -00 , 00 ) instead of [ 0 , 00 ) . The Hausdorff moment

problem is again

**similar**but refers to a finite interval of 1250 XII.8 XII .Page 1380

The proof for Oīj is exactly

etc. , be as in Theorem 18 . Then an isolated point do e do ( T ) is an isolated

singularity of 0 ( or , equivalently , of 0ī ) . Moreover , Pisl { 2 , } ) is the residue at

ho of ...

The proof for Oīj is exactly

**similar**. Q.E.D. 30 COROLLARY . Let t , T , 1 , 0 ;, o ,etc. , be as in Theorem 18 . Then an isolated point do e do ( T ) is an isolated

singularity of 0 ( or , equivalently , of 0ī ) . Moreover , Pisl { 2 , } ) is the residue at

ho of ...

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### Contents

BAlgebras | 859 |

Bounded Normal Operators in Hilbert Space | 887 |

Miscellaneous Applications | 937 |

Copyright | |

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