Linear Operators: General theory |
From inside the book
Results 1-3 of 73
Page 224
Functions of a Complex Variable In some of the chapters to follow , and especially in Chapter VII , we shall use extensions of certain well - known results in the theory of analytic functions of a complex variable to the case where the ...
Functions of a Complex Variable In some of the chapters to follow , and especially in Chapter VII , we shall use extensions of certain well - known results in the theory of analytic functions of a complex variable to the case where the ...
Page 230
If no 20 is The largest number n such that a_inl # 0 is called the order of the pole ар with p < 0 is non - zero , and if we put f ( 20 ) = do , then f becomes analytic in z - zo ! < r , so that the singularity at z = removable .
If no 20 is The largest number n such that a_inl # 0 is called the order of the pole ар with p < 0 is non - zero , and if we put f ( 20 ) = do , then f becomes analytic in z - zo ! < r , so that the singularity at z = removable .
Page 586
Then there exists a 8 > 0 such that if \ ul < d , then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) ) is an analytic function of u for each 1 € U. PROOF . By Lemma 3 , there is a & such that if sul < 81 , then U CO ( T ( u ) ) .
Then there exists a 8 > 0 such that if \ ul < d , then Ū CO ( T ( u ) ) and R ( 2 ; T ( u ) ) is an analytic function of u for each 1 € U. PROOF . By Lemma 3 , there is a & such that if sul < 81 , then U CO ( T ( u ) ) .
What people are saying - Write a review
We haven't found any reviews in the usual places.
Contents
Preliminary Concepts | 1 |
The VitaliHahnSaks Theorem and Spaces of Measures | 7 |
B Topological Preliminaries | 10 |
Copyright | |
91 other sections not shown
Other editions - View all
Common terms and phrases
Akad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed closure complex condition Consequently contains continuous functions converges Corollary defined DEFINITION denote dense determined differential disjoint element equation equivalent everywhere Exercise exists extension field finite follows formula function f given Hence Hilbert space implies integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space linear topological space Math means measure space metric space neighborhood norm open set operator problem Proc projection Proof properties proved range reflexive respect Russian satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero