Linear Operators: General theory |
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Page 363
... kernels Km ( x , y ) . Show that for fe L1 Tmf 1 m - 1 -- Σ 5,1 m j = 0 where S , and Tm have their earlier meanings ... kernel of Exercise 46 is Pr ( x , y ) = 1 = 1-2 { ( 27 ) -1 / 2eina ) . Show that 2л 1 + r2 - 2r cos ( x - y ) Show ...
... kernels Km ( x , y ) . Show that for fe L1 Tmf 1 m - 1 -- Σ 5,1 m j = 0 where S , and Tm have their earlier meanings ... kernel of Exercise 46 is Pr ( x , y ) = 1 = 1-2 { ( 27 ) -1 / 2eina ) . Show that 2л 1 + r2 - 2r cos ( x - y ) Show ...
Page 506
... kernel which has many properties not enjoyed by the kernels of Theorems 2 , 6 , and 7. In this case , the kernel is a bounded u - measurable function ( ) and thus the vector function x ( · ) f ( ) is μ - integrable for every ƒ in L1 ( S ...
... kernel which has many properties not enjoyed by the kernels of Theorems 2 , 6 , and 7. In this case , the kernel is a bounded u - measurable function ( ) and thus the vector function x ( · ) f ( ) is μ - integrable for every ƒ in L1 ( S ...
Page 716
... kernel e ,, and that as time increases the dissipative part is evacuated . Moreover , the kernels e , cannot be decomposed into small- er sets with the first mentioned property . However , each kernel e i can be further split into a ...
... kernel e ,, and that as time increases the dissipative part is evacuated . Moreover , the kernels e , cannot be decomposed into small- er sets with the first mentioned property . However , each kernel e i can be further split into a ...
Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
Algebraic Preliminaries | 34 |
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A₁ Acad additive set function algebra Amer analytic arbitrary B-space B₁ 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 ergodic exists f₁ finite dimensional function defined function f 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-integrable u-measurable uniformly weak topology weakly compact weakly sequentially compact zero ΕΕΣ