## Linear Operators: General theory |

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Page 736

On a method of

SSSR ( N . S . ) 72 , 667 – 670 ( 1950 ) . ( Russian ) Math . Rev . 12 , 183 ( 1951 )

. Bari ( Bary ) , N . K . 1 . Biorthogonal systems and bases in Hilbert space .

On a method of

**solution**of the equation of heat conduction . Doklady Akad . NaukSSSR ( N . S . ) 72 , 667 – 670 ( 1950 ) . ( Russian ) Math . Rev . 12 , 183 ( 1951 )

. Bari ( Bary ) , N . K . 1 . Biorthogonal systems and bases in Hilbert space .

Page 762

Amer . J . Math . 75 , 229 - 240 ( 1953 ) . 3 . The Lg -

equations of second order . Duke Math . J . 14 , 323 – 326 ( 1947 ) . Unrestricted

Amer . J . Math . 75 , 229 - 240 ( 1953 ) . 3 . The Lg -

**solutions**of linear differentialequations of second order . Duke Math . J . 14 , 323 – 326 ( 1947 ) . Unrestricted

**solution**fields of almost separable differential equations . Trans . Amer . Math .Page 763

Acad . Sci . U . S . A . 33 , 376 - 379 ( 1947 ) . 3 . The asymptotic arcus variation of

, 1 - 10 ( 1948 ) . Criteria for the non - degeneracy of the wave equation . Amer .

Acad . Sci . U . S . A . 33 , 376 - 379 ( 1947 ) . 3 . The asymptotic arcus variation of

**solutions**of real linear differential equations of second order . Amer . J . Math . 70, 1 - 10 ( 1948 ) . Criteria for the non - degeneracy of the wave equation . Amer .

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### Contents

B Topological Preliminaries | 10 |

quences | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

80 other sections not shown

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### Common terms and phrases

Acad algebra Amer analytic applied arbitrary assumed B-space Banach Banach spaces bounded called clear closed compact complex condition contains continuous functions converges convex Corollary countably additive defined DEFINITION denote dense determined differential disjoint Doklady Akad element equation equivalent everywhere Exercise exists extension field finite follows function defined function f given Hence Hilbert space implies inequality integral interval isomorphism Lebesgue Lemma limit linear functional linear operator linear space mapping Math meaning measure space metric neighborhood norm operator positive measure problem Proc PROOF properties proved respect Russian satisfies scalar seen semi-group separable sequence set function Show shown sphere statement subset sufficient Suppose Theorem theory topological space topology transformations u-measurable uniform uniformly unique unit valued vector weak weakly compact zero