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Logarithmic and antilogarithmic mappings

100%

Przeworska-Rolewicz D.

Instytut Matematyczny Polskiej Akademii Nauk

CONTENTS Introduction............................................................................................................................................5 0. Preliminaries.......................................................................................................................................6 1. Basic equation. Logarithms and antilogarithms..................................................................................8 2. Logarithms and antilogarithms of higher order.................................................................................19 3. Reduction theorems..........................................................................................................................24 4. Multiplicative case.............................................................................................................................36 5. Leibniz case.......................................................................................................................................41 6. Exponential, power and polylogarithmic functions.............................................................................51 7. Complex case....................................................................................................................................57 8. Smooth logarithms and antilogarithms..............................................................................................64 9. Logarithmic and antilogarithmic mappings induced by left invertible and invertible operators...........70 10. Other generalizations.......................................................................................................................82 References...........................................................................................................86

Two centuries of the term "algebraic analysis"

93%

Przeworska-Rolewicz D.

Banach Center Publications

2000

tom 53

nr 1

47-70

The term "Algebraic Analysis" in the last two decades is used in two completely different senses. It seems that at least one is far away from its historical roots. Thus, in order to explain this misunderstanding, the history of this term from its origins is recalled.

Review: I. H. Dimovski; Convolution Calculus

93%

Przeworska-Rolewicz D.

Mathematica Applicanda

1985

tom 13

nr 25

Artykuł nie zawiera streszczenia

The article contains no abstract

Fourier-like methods for equations with separable variables

93%

Przeworska-Rolewicz D.

Discussiones Mathematicae, Differential Inclusions, Control and Optimization

2009

tom 29

nr 1

19-42

It is well known that a power of a right invertible operator is again right invertible, as well as a polynomial in a right invertible operator under appropriate assumptions. However, a linear combination of right invertible operators (in particular, their sum and/or difference) in general is not right invertible. It will be shown how to solve equations with linear combinations of right invertible operators in commutative algebras using properties of logarithmic and antilogarithmic mappings. The used method is, in a sense, a kind of the variables separation method. We shall obtain also an analogue of the classical Fourier method for partial differential equations. Note that the results concerning the Fourier method are proved under weaker assumptions than these obtained in [6] (cf. also [7, 8, 11]).

Preface, Contents, List of Participants, List of Lectures

41%

Przeworska-Rolewicz D.

Banach Center Publications

2000

tom 53

nr 1

1-10