Linear Operators: General theory |
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Page 414
... boundary point of K ; it remains to show that if the convex set K has at least one interior point p , an internal point q1 is an interior point , and a boundary point 2 is a bounding point . 1 Since q is internal , the vector rep + ( 1 ...
... boundary point of K ; it remains to show that if the convex set K has at least one interior point p , an internal point q1 is an interior point , and a boundary point 2 is a bounding point . 1 Since q is internal , the vector rep + ( 1 ...
Page 777
... boundary value problem of even order in the interval ( 0 , ∞ ) . Doklady Akad . Nauk SSSR ( N. S. ) 74 , 9-12 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ( 1951 ) . 14. Solution of the inverse Sturm - Liouville problem . Doklady Akad ...
... boundary value problem of even order in the interval ( 0 , ∞ ) . Doklady Akad . Nauk SSSR ( N. S. ) 74 , 9-12 ( 1950 ) . ( Russian ) Math . Rev. 12 , 502 ( 1951 ) . 14. Solution of the inverse Sturm - Liouville problem . Doklady Akad ...
Page 818
... boundary conditions . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 433–436 ( 1949 ) . ( Russian ) Math . Rev. 11 , 38-39 ( 1950 ) . 3 . 2. On linear boundary problems for differential equations . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 785 ...
... boundary conditions . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 433–436 ( 1949 ) . ( Russian ) Math . Rev. 11 , 38-39 ( 1950 ) . 3 . 2. On linear boundary problems for differential equations . Doklady Akad . Nauk SSSR ( N. S. ) 65 , 785 ...
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