## Linear Operators: Spectral operators |

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Page 2325

5 and from

16 ) , and

representation m = 1 Śm ~ 2019 + & + z2 + Smn - m , and that the zero & n of M (

u ) ...

5 and from

**formulas**( 16 ) and ( 14 ) . It also follows , from Lemma 3 . 5 ,**formula**(16 ) , and

**formula**( 14 ) , that the zero Šn of M ( u ) in RM has the asymptoticrepresentation m = 1 Śm ~ 2019 + & + z2 + Smn - m , and that the zero & n of M (

u ) ...

Page 2330

Since Gu is analytic by

and Šm of the contour integral ( 27 ) - 1 R ( um ; T ) — nun - 1 Gu ) du . By Lemma

3 , if we take any sufficiently small ε > 0 , and let om denote the circle with radius ε

...

Since Gu is analytic by

**formula**( 21 ) , we have only to take the residues at Émand Šm of the contour integral ( 27 ) - 1 R ( um ; T ) — nun - 1 Gu ) du . By Lemma

3 , if we take any sufficiently small ε > 0 , and let om denote the circle with radius ε

...

Page 2341

We wish to show , using

over all finite sets of integers , is uniformly bounded . This follows from ( 58 ) by

an argument using Lemma 7 , which is similar to the corresponding argument ...

We wish to show , using

**formula**( 58 ) , that the family of all sums MEJ J rangingover all finite sets of integers , is uniformly bounded . This follows from ( 58 ) by

an argument using Lemma 7 , which is similar to the corresponding argument ...

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### Contents

SPECTRAL OPERATORS | 1924 |

Spectral Operators | 1925 |

Terminology and Preliminary Notions | 1928 |

Copyright | |

31 other sections not shown

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