## Linear Operators, Part 1 |

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Page 564

w 19 Find the most general solution of the differential

the matrix of Exercise 5. The next ten exercises refer to the stability theory of

systems of n linear homogeneous differential

...

w 19 Find the most general solution of the differential

**equation**y' = Ty where T isthe matrix of Exercise 5. The next ten exercises refer to the stability theory of

systems of n linear homogeneous differential

**equations**, dy(t)/dt = A(t)\,. Here A(t)...

Page 736

On a method of solution of the

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. Moskov. Gos.

Univ.

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. Moskov. Gos.

Univ.

Page 762

On a class of linear

. SSR 13, 65–72 (1952). (Russian) Math. Rev. 14, 990 (1953). 2. On a class of

linear

...

On a class of linear

**equations**in Hilbert spaces. Soobséeniya Akad. Nauk Gruzin. SSR 13, 65–72 (1952). (Russian) Math. Rev. 14, 990 (1953). 2. On a class of

linear

**equations**with symmetrizable operators. Doklady Akad. Nauk SSSR (N. S.)...

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### Contents

A Settheoretic Preliminaries | 1 |

Convergence and Uniform Convergence of Generalized | 26 |

Algebraic Preliminaries | 34 |

Copyright | |

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additive set function algebra Amer analytic arbitrary B-space Banach baſs Borel sets ca(S Cauchy sequence compact Hausdorff space compact operator complete complex numbers conditionally compact contains continuous functions convex set Corollary countably additive DEFINITION denote dense differential Doklady Akad element equation equivalent exists finite dimensional function defined function f g-field g-finite Hausdorff space Hence Hilbert space homeomorphism implies inequality integral interval isometric isomorphism Lebesgue measure Lemma Let f lim ſº linear map linear operator linear topological space Lp(S Math measurable functions measure space metric space Nauk SSSR N.S. neighborhood non-negative normed linear space open set operator topology positive measure space Proc properties proved real numbers Riesz scalar semi-group sequentially compact Show subset subspace Suppose theory TM(S topological space u-integrable u-measurable uniformly valued function weak topology weakly compact weakly sequentially compact zero