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]).
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1102,
author = {Danuta Przeworska-Rolewicz},
title = {Fourier-like methods for equations with separable variables},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {29},
year = {2009},
pages = {19-42},
zbl = {1205.47010},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1102}
}
Danuta Przeworska-Rolewicz. Fourier-like methods for equations with separable variables. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 29 (2009) pp. 19-42. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1102/
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