Solvability of Infinite Linear Systems

Bruno de Malafosse (), Eberhard Malkowsky and Vladimir Rakočević
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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

Chapter Chapter 7 in Operators Between Sequence Spaces and Applications, 2021, pp 315-358 from Springer

Abstract: 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.

Date: 2021
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DOI: 10.1007/978-981-15-9742-8_7

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