# Algebraic and analytic properties of solutions of abstract differential equations

• Publisher: Instytut Matematyczny Polskiej Akademi Nauk(Warszawa), 1964

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## Abstract

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CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions................................................................................................................................. 5§ 2. Fundamental system of solving operations in linear spaces and algebras1. Operational independence and solving operations.......................................................... 82. One linear differential equation of the first order................................................................. 93. A system of linear differential equations of the first order............................................... 114. Linear differential equations of order n.............................................................................. 155. Partial derivatives..................................................................................................................... 186. Linear partial differential equations...................................................................................... 207. Wroński’s fundamentality criteria in algebras................................................................. 248. Examples................................................................................................................................ 25§ 3. Universal spaces of analytic elements1. Introduction............................................................................................................................. 262. The space ${C}_{N}\left(ℬ\right)$........................................................................................................... 273. Multiplications, superposition and convolution of elementsof ${C}_{N}\left(ℬ\right)$.................................................................................................................................. 294. The space ${C}_{N}^{m}\left(ℬ\right)$ of analytic functions of many multipliers................................. 326. Examples.................................................................................................................................. 33Chapter II. ANALYTIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 4. Existence, uniqueness and continuity of solutions1. Regular operations in ${K}_{Z}$-linear spaces....................................................................... 352. The well-defined problem of solution of an abstract differential equation.................... 373. Examples................................................................................................................................... 41§ 5. Analytic elements1. Introduction.............................................................................................................................. 43§ 6. The separation of variables1. The separation of variables.................................................................................................. 462. Examples................................................................................................................................. 49§ 7. Summation theorem1. The Kojima-Schur and the Toeplitz theorems................................................................. 522. Euler’s theorems..................................................................................................................... 643. Newton’s interpolation formulas........................................................................................ 554. Examples................................................................................................................................. 59REFERENCES............................................................................................................................ 61

## How to cite

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R. Bittner. Algebraic and analytic properties of solutions of abstract differential equations. Warszawa: Instytut Matematyczny Polskiej Akademi Nauk, 1964. <http://eudml.org/doc/268604>.

@book{R1964,
abstract = {CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions................................................................................................................................. 5§ 2. Fundamental system of solving operations in linear spaces and algebras1. Operational independence and solving operations.......................................................... 82. One linear differential equation of the first order................................................................. 93. A system of linear differential equations of the first order............................................... 114. Linear differential equations of order n.............................................................................. 155. Partial derivatives..................................................................................................................... 186. Linear partial differential equations...................................................................................... 207. Wroński’s fundamentality criteria in algebras................................................................. 248. Examples................................................................................................................................ 25§ 3. Universal spaces of analytic elements1. Introduction............................................................................................................................. 262. The space $C_N(ℬ)$........................................................................................................... 273. Multiplications, superposition and convolution of elementsof $C_N(ℬ)$.................................................................................................................................. 294. The space $C_N^m(ℬ)$ of analytic functions of many multipliers................................. 326. Examples.................................................................................................................................. 33Chapter II. ANALYTIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 4. Existence, uniqueness and continuity of solutions1. Regular operations in $K_Z$-linear spaces....................................................................... 352. The well-defined problem of solution of an abstract differential equation.................... 373. Examples................................................................................................................................... 41§ 5. Analytic elements1. Introduction.............................................................................................................................. 43§ 6. The separation of variables1. The separation of variables.................................................................................................. 462. Examples................................................................................................................................. 49§ 7. Summation theorem1. The Kojima-Schur and the Toeplitz theorems................................................................. 522. Euler’s theorems..................................................................................................................... 643. Newton’s interpolation formulas........................................................................................ 554. Examples................................................................................................................................. 59REFERENCES............................................................................................................................ 61},
author = {R. Bittner},
keywords = {functional analysis},
language = {eng},
location = {Warszawa},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
title = {Algebraic and analytic properties of solutions of abstract differential equations},
url = {http://eudml.org/doc/268604},
year = {1964},
}

TY - BOOK
AU - R. Bittner
TI - Algebraic and analytic properties of solutions of abstract differential equations
PY - 1964
CY - Warszawa
PB - Instytut Matematyczny Polskiej Akademi Nauk
AB - CONTENTSINTRODUCTION............................................................................................................................... 3Chapter I. ALGEBRAIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 1. Ordinary abstract differential equations1. Taylor’s formula for an abstract derivative.......................................................................... 42 π-solutions................................................................................................................................. 5§ 2. Fundamental system of solving operations in linear spaces and algebras1. Operational independence and solving operations.......................................................... 82. One linear differential equation of the first order................................................................. 93. A system of linear differential equations of the first order............................................... 114. Linear differential equations of order n.............................................................................. 155. Partial derivatives..................................................................................................................... 186. Linear partial differential equations...................................................................................... 207. Wroński’s fundamentality criteria in algebras................................................................. 248. Examples................................................................................................................................ 25§ 3. Universal spaces of analytic elements1. Introduction............................................................................................................................. 262. The space $C_N(ℬ)$........................................................................................................... 273. Multiplications, superposition and convolution of elementsof $C_N(ℬ)$.................................................................................................................................. 294. The space $C_N^m(ℬ)$ of analytic functions of many multipliers................................. 326. Examples.................................................................................................................................. 33Chapter II. ANALYTIC PROPERTIES OF SOLUTIONS OF ABSTRACT DIFFERENTIALEQUATIONS§ 4. Existence, uniqueness and continuity of solutions1. Regular operations in $K_Z$-linear spaces....................................................................... 352. The well-defined problem of solution of an abstract differential equation.................... 373. Examples................................................................................................................................... 41§ 5. Analytic elements1. Introduction.............................................................................................................................. 43§ 6. The separation of variables1. The separation of variables.................................................................................................. 462. Examples................................................................................................................................. 49§ 7. Summation theorem1. The Kojima-Schur and the Toeplitz theorems................................................................. 522. Euler’s theorems..................................................................................................................... 643. Newton’s interpolation formulas........................................................................................ 554. Examples................................................................................................................................. 59REFERENCES............................................................................................................................ 61
LA - eng
KW - functional analysis
UR - http://eudml.org/doc/268604
ER -

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