Linear Operators: General theory |
From inside the book
Results 1-3 of 29
Page 614
... semi - group of operators in X ; i.e. , a family of operators satisfying the conditions of the following definition . 1 DEFINITION . A family { T ( t ) } , 0 ≤t < ∞ , of bounded linear operators in X will be called a strongly continuous ...
... semi - group of operators in X ; i.e. , a family of operators satisfying the conditions of the following definition . 1 DEFINITION . A family { T ( t ) } , 0 ≤t < ∞ , of bounded linear operators in X will be called a strongly continuous ...
Page 655
... semi- group on [ 0 , ∞ ) . Equivalently , T ( t ) ( x , s ) = ∞ xe - n2 + ins if x ( s ) ~ eins . Show that the infinitesimal generator of the semi- group T ( t ) is the operator A whose domain D ( A ) consists of all periodic ...
... semi- group on [ 0 , ∞ ) . Equivalently , T ( t ) ( x , s ) = ∞ xe - n2 + ins if x ( s ) ~ eins . Show that the infinitesimal generator of the semi- group T ( t ) is the operator A whose domain D ( A ) consists of all periodic ...
Page 694
... semi - groups need not commute , for if they do commute then T ( t1 , . . . , tx ) Ta ( t ) ... Ti ( t ) is a k - parameter semi - group . = 10 THEOREM . Let the semi - groups ( T , ( t ) , 0 ≤ t } , i = 1 , ... , k , be strongly ...
... semi - groups need not commute , for if they do commute then T ( t1 , . . . , tx ) Ta ( t ) ... Ti ( t ) is a k - parameter semi - group . = 10 THEOREM . Let the semi - groups ( T , ( t ) , 0 ≤ t } , i = 1 , ... , k , be strongly ...
Contents
8 | 28 |
Algebraic Preliminaries | 34 |
Three Basic Principles of Linear Analysis | 49 |
Copyright | |
40 other sections not shown
Other editions - View all
Common terms and phrases
A₁ additive set function algebra Amer analytic arbitrary B-space ba(S Banach Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense differential disjoint Doklady Akad E₁ element equation exists f₁ finite dimensional function defined function f Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism L₁ L₁(S Lebesgue Lemma Let f linear map linear operator linear topological space Math measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative normed linear space o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ