Linear Operators: General theory |
From inside the book
Results 1-3 of 74
Page 224
... analytic functions of a complex variable to the case where the func- tions are vector valued . It will be assumed that the reader is familiar with the elementary theory of complex valued analytic functions of one complex variable and ...
... analytic functions of a complex variable to the case where the func- tions are vector valued . It will be assumed that the reader is familiar with the elementary theory of complex valued analytic functions of one complex variable and ...
Page 228
... analytic on an open set U in the space of the complex variables 21 , .. , zn . Let V be a bounded open subset of U whose closure is contained in U. If fn converges at each point of U to a function f on U then f is analytic in U , and ...
... analytic on an open set U in the space of the complex variables 21 , .. , zn . Let V be a bounded open subset of U whose closure is contained in U. If fn converges at each point of U to a function f on U then f is analytic in U , and ...
Page 230
... analytic in z - zor , so that the singularity at z = zo is removable . If a , 0 for p≤0 , % is called a zero of f ... analytic on a domain U in the space of n complex variables , and let g be an analytic function defined on a do- main V ...
... analytic in z - zor , so that the singularity at z = zo is removable . If a , 0 for p≤0 , % is called a zero of f ... analytic on a domain U in the space of n complex variables , and let g be an analytic function defined on a do- main V ...
Contents
A Settheoretic Preliminaries | 1 |
10 | 30 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
31 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra analytic arbitrary B-space B₁ ba(S Banach Borel sets ca(S Cauchy sequence closed unit sphere compact Hausdorff space compact operator complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense E₁ element equation equivalent exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue measure Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space neighborhood non-negative non-zero normed linear space o-field o-finite open set operator topology positive measure space properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact X₁ zero ΕΕΣ