## Linear Operators: Spectral operators |

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Page 2323

If Regularity

1 + . . + do , ap + 0 , ( 13 ) 772 ( g ) = bp + bp - 142 - 1 + . . . + bo , bp # 0 , TT3 ( x )

= C , HP + cp - 1u2 - + + Co . The labor of verifying

If Regularity

**Hypothesis**1 is satisfied , we may write TT1 ( u ) = ap leo + ap - 148 -1 + . . + do , ap + 0 , ( 13 ) 772 ( g ) = bp + bp - 142 - 1 + . . . + bo , bp # 0 , TT3 ( x )

= C , HP + cp - 1u2 - + + Co . The labor of verifying

**Hypothesis**1 may be ...Page 2418

Therefore

subdomain D of the complex plane is not dense in the complex plane , there

exists a complex number do whose distance from the domain D exceeds a

certain ...

Therefore

**hypothesis**( c ) of Theorem 8 is verified . Since by**hypothesis**thesubdomain D of the complex plane is not dense in the complex plane , there

exists a complex number do whose distance from the domain D exceeds a

certain ...

Page 2449

On the other hand , assuming the truth of our assertion for a given n , it follows

from ( 6 ) that tn + 1 Sty + 6M2tį . Since , by

= 2t , and our assertion follows . It also follows from ( 5 ) and

...

On the other hand , assuming the truth of our assertion for a given n , it follows

from ( 6 ) that tn + 1 Sty + 6M2tį . Since , by

**hypothesis**, 6M2tı 51 , we have tn + 1= 2t , and our assertion follows . It also follows from ( 5 ) and

**hypotheses**( d ) and...

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