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Page 738
Boundary value and expansion problems of ordinary linear differential equations . Trans . Amer . Math . Soc . 9 , 373–395 ( 1908 ) . 4. Existence and oscillation theorems for a certain boundary value problem . Trans . Amer . Math .
Boundary value and expansion problems of ordinary linear differential equations . Trans . Amer . Math . Soc . 9 , 373–395 ( 1908 ) . 4. Existence and oscillation theorems for a certain boundary value problem . Trans . Amer . Math .
Page 780
On the detection of the oscillation of a second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . 4. On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33–47 ( 1952 ) .
On the detection of the oscillation of a second order linear differential equation . Duke Math . J. 17 , 57-62 ( 1950 ) . 4. On self - adjoint differential equations of second order . J. London Math . Soc . 27 , 33–47 ( 1952 ) .
Page 781
The application of generalized displacement operators to linear differential equations of the second order . Uspehi Matem . Nauk ( N. S. ) 4 , no . 1 ( 29 ) , 3–112 ( 1949 ) . ( Russian ) Math . Rev. 11 , 116 ( 1950 ) . Amer . Math .
The application of generalized displacement operators to linear differential equations of the second order . Uspehi Matem . Nauk ( N. S. ) 4 , no . 1 ( 29 ) , 3–112 ( 1949 ) . ( Russian ) Math . Rev. 11 , 116 ( 1950 ) . Amer . Math .
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Contents
Preliminary Concepts | 1 |
B Topological Preliminaries | 10 |
quences | 26 |
Copyright | |
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Akad algebra Amer analytic applied arbitrary assume B-space Banach Banach spaces bounded called clear closed compact complex Consequently contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math mean measure space metric space neighborhood norm o-field open set operator positive problem Proc PROOF properties proved range regular respect Russian satisfies scalar seen separable sequence set function Show shown sphere statement subset Suppose Theorem theory topological space topology transformations u-integrable u-measurable uniformly union unique unit valued vector weak zero