Linear Operators: General theory |
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Page 762
... second order . Duke Math . J. 14 , 323-326 ( 1947 ) . 4. Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . 5. On differential equations with non - oscillatory ...
... second order . Duke Math . J. 14 , 323-326 ( 1947 ) . 4. Unrestricted solution fields of almost separable differential equations . Trans . Amer . Math . Soc . 63 , 560-580 ( 1948 ) . 5. On differential equations with non - oscillatory ...
Page 780
... second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . Leja , F. 1. Sur la notion du groupe abstrait ...
... second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33-47 ( 1952 ) . Leja , F. 1. Sur la notion du groupe abstrait ...
Page 794
... second kind of a symmetric operator . Izvestiya Akad . Nauk SSSR 4 , 53-104 ... order . Doklady Akad . Nauk SSSR ( N. S. ) 85 , 41-44 ( 1952 ) . ( Russian ) ... second order . Uspehi Matem . Nauk ( N. S. ) 8 , no . 4 ( 56 ) , 174–175 ( 1953 ) ...
... second kind of a symmetric operator . Izvestiya Akad . Nauk SSSR 4 , 53-104 ... order . Doklady Akad . Nauk SSSR ( N. S. ) 85 , 41-44 ( 1952 ) . ( Russian ) ... second order . Uspehi Matem . Nauk ( N. S. ) 8 , no . 4 ( 56 ) , 174–175 ( 1953 ) ...
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