## Linear Operators: General theory |

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Page 738

Boundary value and expansion problems of ordinary linear

. Trans . Amer . Math . Soc . 9 , 373 – 395 ( 1908 ) . 4 . Existence and oscillation

theorems for a certain boundary value problem . Trans . Amer . Math . Soc .

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 . Soc .

Page 780

Nelson Dunford, Jacob T. Schwartz. 3 . On the detection of the oscillation of a

second order linear

On self - adjoint

Nelson Dunford, Jacob T. Schwartz. 3 . 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 .Page 781

The application of generalized displacement operators to linear

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 . Soc .

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 . Soc .

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### Contents

Preliminary Concepts | 1 |

B Topological Preliminaries | 10 |

Algebraic Preliminaries | 34 |

Copyright | |

31 other sections not shown

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### Common terms and phrases

algebra Amer analytic applied arbitrary assumed B-space Banach spaces bounded called clear closed compact operator complex condition Consequently constant contains continuous functions converges convex convex set Corollary countably additive defined DEFINITION denote dense determined differential dimensional disjoint domain element equation equivalent everywhere Exercise exists extension field finite follows formula function defined function f given Hence Hilbert space identity implies inequality integral interval Lebesgue Lemma limit linear functional linear operator linear space Math neighborhood norm operator operator topology problem projection PROOF properties proved range reflexive representation respect satisfies scalar seen semi-group separable sequence set function Show shown statement subset subspace sufficient Suppose Theorem theory topology u-measurable uniform uniformly unique unit sphere valued vector weak weakly compact zero