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Connection of Solutions of Abstract Paired Equations in Rings with Factorization Pairs

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Modern Analysis and Applications

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 191))

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Abstract

The connection between solutions of the abstract paired equations with respect to an unknown \( x \in \left( {R_1 \cap R_2 } \right) \):

$$ \left\{ {\begin{array}{*{20}c} {\left( {a_1 x} \right)^ - = c^ - ,} \\ {\left( {a_2 x} \right)^ + = b^ + ,} \\ \end{array} } \right. $$

is considered. It is assumed that the coefficients a j ∈ R j , j = 1, 2, where R 1 , R 2 are the associative rings with factorization pairs \( \left( {R_j^ + ,R_j^ - } \right) \) and unity \( e \in R_1 \cap R_2 \).

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Authors and Affiliations

  1. Department of High Mathematics Odessa State Academy of Buildings and Architecture, 4 Didrihsona St., 65029, Odessa, Ukraine

    Gennadiy Poletaev

Authors
  1. Gennadiy Poletaev
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Editor information

Editors and Affiliations

  1. Department of Theoretical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Vadim M. Adamyan

  2. Department of Mathematical Sciences Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, 69978, Ramat Aviv, Israel

    Israel Gohberg

  3. Insitute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivska st., 01601, Kyiv-4, Ukraine

    Anatoly Kochubei , Yurij Berezansky , Myroslav Gorbachuk  & Valentyna Gorbachuk , ,  & 

  4. Department of Mathematical Physics, Odessa National I.I. Mechnikov University, Dvoryanska st. 2, 65026, Odessa, Ukraine

    Gennadiy Popov

  5. Institute of Analysis and Scientific Computing, Technical University of Vienna, Wiedner Hauptstrasse 8-10, 1040, Vienna, Austria

    Heinz Langer

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© 2009 Birkhäuser Verlag Basel/Switzerland

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Poletaev, G. (2009). Connection of Solutions of Abstract Paired Equations in Rings with Factorization Pairs. In: Adamyan, V.M., et al. Modern Analysis and Applications. Operator Theory: Advances and Applications, vol 191. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-9921-4_29

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