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Algebraic and analytic properties of solutions of abstract differential equations

100%

Bittner R.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS INTRODUCTION............................................................................................................................... 3 Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIAL EQUATIONS § 1. Ordinary abstract differential equations 1. Taylor’s formula for an abstract derivative.......................................................................... 4 2 π-solutions................................................................................................................................. 5 § 2. Fundamental system of solving operations in linear spaces and algebras 1. Operational independence and solving operations.......................................................... 8 2. One linear differential equation of the first order................................................................. 9 3. A system of linear differential equations of the first order............................................... 11 4. Linear differential equations of order n.............................................................................. 15 5. Partial derivatives..................................................................................................................... 18 6. Linear partial differential equations...................................................................................... 20 7. Wroński's fundamentality criteria in algebras................................................................. 24 8. Examples................................................................................................................................ 25 § 3. Universal spaces of analytic elements 1. Introduction............................................................................................................................. 26 2. The space $C_N(ℬ)$........................................................................................................... 27 3. Multiplications, superposition and convolution of elements of $C_N(ℬ)$.................................................................................................................................. 29 4. The space $C_N^m(ℬ)$ of analytic functions of many multipliers................................. 32 6. Examples.................................................................................................................................. 33 Chapter II. ANALYTIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIAL EQUATIONS § 4. Existence, uniqueness and continuity of solutions 1. Regular operations in $K_Z$-linear spaces....................................................................... 35 2. The well-defined problem of solution of an abstract differential equation.................... 37 3. Examples................................................................................................................................... 41 § 5. Analytic elements 1. Introduction.............................................................................................................................. 43 § 6. The separation of variables 1. The separation of variables.................................................................................................. 46 2. Examples................................................................................................................................. 49 § 7. Summation theorem 1. The Kojima-Schur and the Toeplitz theorems................................................................. 52 2. Euler’s theorems..................................................................................................................... 64 3. Newton’s interpolation formulas........................................................................................ 55 4. Examples................................................................................................................................. 59 REFERENCES............................................................................................................................ 61

Operational calculus in linear spaces

25%

Bittner R.

Studia Mathematica

1961

tom 20

nr 1

1-18

Ograniczanie wyników

1 Studia Mathematica

2 Bittner R.

1 1964

1 1961

Wyniki wyszukiwania

Algebraic and analytic properties of solutions of abstract differential equations

Operational calculus in linear spaces