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Solvability of Infinite Linear Systems

In: Operators Between Sequence Spaces and Applications

Author

Listed:
  • Bruno de Malafosse

    (University of Le Havre (LMAH))

  • Eberhard Malkowsky

    (Univerzitet Union Nikola Tesla, Faculty of Management)

  • Vladimir Rakočević

    (University of Niš, Department of Mathematics)

Abstract

In Chapter 7, we apply the previous results on summability and study infinite systems with linear equations. So, we obtain some results in the spectral theory. Notice that this domain has a lot of applications in numerical analysis, aeronautic, quantum mechanics, ecology, electrical engineering, structural mechanics and probability. Then, we deal with the famous Hill equation and we consider a Banach algebra in which we may obtain the inverse of an infinite matrix and obtain a new method to calculate the Floquet exponent. Then, we determine the solutions of the infinite linear system associated with the Hill equation with a second member and give a method to approximate them. In a similar way, there is a study of the Mathieu equation which can be written as an infinite tridiagonal linear system of equations.

Suggested Citation

  • Bruno de Malafosse & Eberhard Malkowsky & Vladimir Rakočević, 2021. "Solvability of Infinite Linear Systems," Springer Books, in: Operators Between Sequence Spaces and Applications, chapter 0, pages 315-358, Springer.
    • Handle: RePEc:spr:sprchp:978-981-15-9742-8_7
    DOI: 10.1007/978-981-15-9742-8_7
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