Linear Operators: General theory |
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Page 226
... integral theo- rem states that So f ( x ) da 0 . The validity of this ... integral theorem may be reworded in a somewhat more gener- al form . To state this ... square mesh , and let U be the union of all open squares of the mesh whose ...
... integral theo- rem states that So f ( x ) da 0 . The validity of this ... integral theorem may be reworded in a somewhat more gener- al form . To state this ... square mesh , and let U be the union of all open squares of the mesh whose ...
Page 469
... integral dxn . 1 ( t ) = f ... ... · С Do ( t ; x ) dx ̧ . . . dỡŋ · S It is ... integral sign and employ [ * ] to conclude that I ' ( t ) is a sum of ... square root { 1 - ( + ... + x + x + 1 + ... + 2 ) } 1/2 , and a denote the ...
... integral dxn . 1 ( t ) = f ... ... · С Do ( t ; x ) dx ̧ . . . dỡŋ · S It is ... integral sign and employ [ * ] to conclude that I ' ( t ) is a sum of ... square root { 1 - ( + ... + x + x + 1 + ... + 2 ) } 1/2 , and a denote the ...
Page 781
... integrable square of the system of differential equations . —y ' ' + P ( t ) y = λy . Doklady Akad . Nauk SSSR ( N. S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1 . On the theory of regular ...
... integrable square of the system of differential equations . —y ' ' + P ( t ) y = λy . Doklady Akad . Nauk SSSR ( N. S. ) 95 , 217-220 ( 1954 ) . ( Russian ) Math . Rev. 15 , 957 ( 1954 ) . Lifšic , I. M. 1 . On the theory of regular ...
Contents
A Settheoretic Preliminaries | 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 Cauchy sequence compact operator complex numbers contains continuous functions continuous linear converges convex set Corollary countably additive DEFINITION denote dense differential equations disjoint Doklady Akad domain E₁ element exists f₁ finite dimensional finite number function defined function f Hausdorff space Hence Hilbert space homeomorphism inequality integral L₁ L₁(S Lebesgue Lemma Let f linear functional linear map linear operator linear topological space measurable function measure space metric space Nauk SSSR N. S. neighborhood non-negative o-field open set operator topology positive measure space Proc PROOF proved real numbers Riesz Russian S₁ scalar semi-group sequentially compact Show spectral strong operator topology subset subspace Suppose T₁ theory topological space u-integrable u-measurable uniformly unit sphere valued function weakly compact zero ΕΕΣ