## Linear Operators: Spectral theory |

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Page 977

By substituting ( for 0 - 4 + ( / 2 ) and simplifying , it is

iem ) " lim f ( r ) rdr 27 R + JO Now the Bessel function Jn of order n is defined by

the equation 1 201 - ei ( n0 — z sin do ; J ( z ) = - 20 Jo e hence we have G ( u , v

) ...

By substituting ( for 0 - 4 + ( / 2 ) and simplifying , it is

**seen**that 27 G ( u , v ) = - ( -iem ) " lim f ( r ) rdr 27 R + JO Now the Bessel function Jn of order n is defined by

the equation 1 201 - ei ( n0 — z sin do ; J ( z ) = - 20 Jo e hence we have G ( u , v

) ...

Page 1037

product clearly converges to zero for 2 = dk it is readily

T ) is analytic for 2 # 0 and vanishes only for 2 in o ( T ) . It remains to show that if

2 + 0 , then Qi ( T ) is continuous in T relative to the Hilbert - Schmidt norm in HS .

product clearly converges to zero for 2 = dk it is readily

**seen**that the function qi (T ) is analytic for 2 # 0 and vanishes only for 2 in o ( T ) . It remains to show that if

2 + 0 , then Qi ( T ) is continuous in T relative to the Hilbert - Schmidt norm in HS .

Page 1154

Since it is clear that E ( 2 ) = { x , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =

c ( 2x2 ) ( E ) , Ee { ( 2 ) , for some constant c independent of E . This condition ( i )

, as is

Since it is clear that E ( 2 ) = { x , what will be proved then , is that ( i ) 2 ( 2 ) ( E ) =

c ( 2x2 ) ( E ) , Ee { ( 2 ) , for some constant c independent of E . This condition ( i )

, as is

**seen**from Corollary III . 11 . 6 , is a consequence of the assertion that ( ii ) ...### What people are saying - Write a review

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### Contents

BAlgebras | 861 |

Commutative BAlgebras | 868 |

Commutative BAlgebras | 874 |

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