Linear Operators: General theory |
From inside the book
Results 1-3 of 71
Page 505
... equation that x * ( s ) = x * ( s ) for μ - almost all s in S. Equation ( ii ) holds for a and therefore equation ( i ) does likewise . Q.E.D. In the following theorem it is shown that if the range of an opera- tor on L1 ( S , E , μ ) ...
... equation that x * ( s ) = x * ( s ) for μ - almost all s in S. Equation ( ii ) holds for a and therefore equation ( i ) does likewise . Q.E.D. In the following theorem it is shown that if the range of an opera- tor on L1 ( S , E , μ ) ...
Page 741
... equations of arbitrary order . Proc . Nat . Acad . Sci . U.S.A. 38 , 741-747 ( 1952 ) . 3. Assumption of boundary values and the Green's function in the Dirichlet problem for the general linear elliptic equation . Proc . Nat . Acad ...
... equations of arbitrary order . Proc . Nat . Acad . Sci . U.S.A. 38 , 741-747 ( 1952 ) . 3. Assumption of boundary values and the Green's function in the Dirichlet problem for the general linear elliptic equation . Proc . Nat . Acad ...
Page 780
... equation . Duke Math . J. 17 , 57-62 ( 1950 ) . Leja , F. On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . 1. Sur la notion du groupe abstrait topologique . Fund . Math . 9 , 37-44 ...
... equation . Duke Math . J. 17 , 57-62 ( 1950 ) . Leja , F. On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . 1. Sur la notion du groupe abstrait topologique . Fund . Math . 9 , 37-44 ...
Contents
A Settheoretic Preliminaries | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
Copyright | |
59 other sections not shown
Other editions - View all
Common terms and phrases
A₁ Acad additive set function algebra Amer analytic arbitrary B-space ba(S Banach spaces Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complex numbers contains continuous functions converges convex set Corollary countably additive DEFINITION dense disjoint Doklady Akad E₁ element exists f₁ finite dimensional function defined function f g₁ Hausdorff space Hence Hilbert space homeomorphism implies inequality integral isometric isomorphism K₁ L₁ L₁(S Lebesgue Lemma Let f linear manifold linear map linear operator linear topological space measurable functions measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field o-finite open set operator topology positive measure space Proc PROOF properties proved real numbers reflexive Riesz S₁ scalar semi-group sequentially compact Show subset subspace Suppose theory topological space u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ