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On the uniqueness of the solution of dual equation of a singular Sturm–Liouville problem

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Abstract

In this paper we consider differential systems having a singularity and one turning point. First, by a replacement, we transform the system to a linear second-order equation of Sturm–Liouville type with a singularity. Using the infinite product representation of solutions provided in [8], we obtain the dual equation, then we investigate the uniqueness of the solution for the dual equation of the inverse spectral problem of Sturm–Liouville equation. This result is necessary for expressing inverse problem of indefinite Sturm–Liouville equation.

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References

  1. Barcilon V, Explicit solution of the inverse problem for a vibrating string, J. Math. Anal. Appl. 93 (1983) 222–234

    Article  MathSciNet  MATH  Google Scholar 

  2. Freiling G and Yurko V, On constructing differential equations with singularities from incomplete spectral information, Inverse Problems 14 (1998) 1131–1150

    Article  MathSciNet  MATH  Google Scholar 

  3. Jodayree Akbarfam A and Mingarelli A B, Duality for indefinite inverse Sturm–Liouville problem, J. Math. Anal. Appl. 312 (2005) 435–463

    Article  MathSciNet  MATH  Google Scholar 

  4. Jodayree Akbarfam A and Mingarelli A B, The canonical product of the solution of the Sturm–Liouville equation in one turning point case, Canad. Appl. Math. Quart. 8(4) (2000) 305–320

    Article  MathSciNet  MATH  Google Scholar 

  5. Kheiri H, Jodayree Akbarfam A and Mingarelli A B, The uniqueness of the solution of dual equations of an inverse indefinite Sturm–Liouville problem, J. Math. Anal. Appl. 306 (2005) 269–281

    Article  MathSciNet  MATH  Google Scholar 

  6. Levin B Ja, Distribution of zeros of entire functions, Transl. Math. Monogr., Amer. Math. Soc. (1964)

  7. Litvinenko O N and Soshnikov V I, The Theory of Heterogenous Lines and their Applications in Radio Engineering (Moscow: Radio, Russian) (1964)

    Google Scholar 

  8. Neamaty A and Mosazadeh S, On the canonical solution of the Sturm–Liouville problem with singularity and turning point of even order, Canad. Math. Bull 54(3) (2011) 506–518, doi:10.4153/CMB-2011-069-7

    MathSciNet  MATH  Google Scholar 

  9. Sveshnikov A G and Il’inskii A S, Design problems in electrodynamics, Dokl. Akad. Nauk SSSR 204(5) (1972) 1077–1080

    Google Scholar 

  10. Tikhonravov A V, The accuracy obtainable in principle when solving synthesis problems, Zh. Vychisl. Mat. Mat. Fiz 22 (1982) 1421–1433

    MathSciNet  Google Scholar 

  11. Yurko V, Spectral analysis for differential operators with singularities, Abstract Appl. Anal. 2 (2004) 165–182

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, University of Mazandaran, Babolsar, Iran

    S MOSAZADEH & A NEAMATY

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  1. S MOSAZADEH
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  2. A NEAMATY
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Correspondence to S MOSAZADEH.

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MOSAZADEH, S., NEAMATY, A. On the uniqueness of the solution of dual equation of a singular Sturm–Liouville problem. Proc Math Sci 121, 469–480 (2011). https://doi.org/10.1007/s12044-011-0044-5

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  • DOI: https://doi.org/10.1007/s12044-011-0044-5

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