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Exact treatment of operator difference equations with nonconstant and noncommutative coefficients

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Abstract

We study a homogeneous linear second-order difference equation with nonconstant and noncommuting operator coefficients in a vector space. We build its exact resolutive formula consisting of the explicit noniterative expression of a generic term of the unknown sequence of vectors. Some nontrivial applications are reported in order to show the usefulness and the broad applicability of the result.

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References

  1. Kelley WG, Peterson AC (2001) Difference equations. In: An introduction with applications, 2nd edn. Harcourt/Academic, Waltham

  2. Driver RD (1977) Ordinary and delay differential equations. Springer, New York

    Book  MATH  Google Scholar 

  3. Azad H, Laradji A, Mustafa MT (2011) Polynomial solutions of differential equations. Adv Differ Equ 58:1–12

    MathSciNet  Google Scholar 

  4. Mallik R (1997) On the solution of a second order linear homogeneous difference equation with variable coefficients. J Math Anal Appl 215(1):32–47

    Article  MathSciNet  MATH  Google Scholar 

  5. Mallik R (1998) Solutions of linear difference equations with variable coeffcients. J Math Anal Appl 222:79–91

    Article  MathSciNet  MATH  Google Scholar 

  6. Napoli A, Messina A, Tretynyk V (2002) Construction of a fundamental set of solutions of an arbitrary homogeneous linear difference equation. Report Math Phys 49(2–3):31–323

    MathSciNet  Google Scholar 

  7. Taher RB, Rachidi M (2001) Linear recurrence relations in the algebra of matrices and applications. Linear algebra appl 330:15–24

    Article  MathSciNet  MATH  Google Scholar 

  8. Jivulescu MA, Messina A, Napoli A (2008) Elementary symmetric functions of two solvents of a quadratic matrix equations. Report Math Phys 62(3):411–429

    MathSciNet  Google Scholar 

  9. Jivulescu MA, Messina A, Napoli A (2010) General solution of a second order non-homogenous linear difference equation with noncommutative coefficients. Appl Math Inform Sci 4(1):1–14

    MathSciNet  MATH  Google Scholar 

  10. Jivulescu MA, Messina A, Napoli A, Petruccione F (2007) Exact treatment of linear difference equations with noncommutative coefficients. Math Methods Appl Sci 30:2147–2153

    Article  MathSciNet  MATH  Google Scholar 

  11. Spiegel M (1998) Schaum’s mathematical handbook of formulas and tables. McGraw-Hill, New York, p 11

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Acknowledgments

This paper was written to honor Peter Leach, a profound scientist and a delightful person. A.M. thanks him and the organizers for the pleasant and warm atmosphere at Salt Rock, Durban, South Africa, in November 2011 on the occasion of Peter’s 70th birthday. M.A.J. gratefully acknowledges the financial support of the Erwin Schrodinger International Institute for Mathematical Physics, where parts of this work were carried out. The authors thank Professor Andrzej Jamiolkowski for carefully reading the manuscript and for useful comments.

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Authors and Affiliations

  1. Department of Mathematics, University “Politehnica” of Timişoara, P-ta Victoriei Nr. 2, 300006 , Timişoara, Romania

    Maria Anastasia Jivulescu

  2. Dipartimento di Fisica, Università di Palermo, via Archirafi 36, 90123 , Palermo, Italy

    Antonino Messina

Authors
  1. Maria Anastasia Jivulescu
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  2. Antonino Messina
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Correspondence to Maria Anastasia Jivulescu.

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Jivulescu, M.A., Messina, A. Exact treatment of operator difference equations with nonconstant and noncommutative coefficients. J Eng Math 82, 149–160 (2013). https://doi.org/10.1007/s10665-012-9602-9

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  • DOI: https://doi.org/10.1007/s10665-012-9602-9

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