ArticleOriginal scientific text
Title
Fourier-like methods for equations with separable variables
Authors 1
Affiliations
- Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, 00-956 Warszawa 10, P.O. Box 21, Poland
Abstract
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]).
Keywords
algebraic analysis, commutative algebra with unit, Leibniz condition, logarithmic mapping, antilogarithmic mapping, right invertible operator, sine mapping, cosine mapping, initial value problem, boundary value problem, Fourier method
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Pages:
19-42
Main language of publication
English
Received
2009-03-03
Published
2009
DOI: 10.7151/dmdico.1102
Exact and natural sciences