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Rational functions of best L p- approximation and analytic continuability

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Abstract

Sufficient conditions for the analytic (resp. meromorphic) continuability of a function f ∈ L p([−1, l]), p > 0, in terms of rational functions of best weighted L p- approximation with an unbounded number of finite poles are established.

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References

  1. R. K. Kovacheva, Uniform convergence of rational sequences of best L p- approximation, Results Math. 36, 1999, 271–280.

    Article  MathSciNet  MATH  Google Scholar 

  2. G. M. Goluzin, Geometric theory of functions of a complex variable, in Russian, Nauka, Moscow, 1966.

  3. A. A. Gonchar, A local condition for the uniqueness of analytic functions, Matem. sbornik 89, 1972, 148–164.

    Google Scholar 

  4. A. Kroo, J. Swetits, On density of interpolation points, a Kadec type theorem and Saff’s principle of contamination in L p- approximation, Constructive Approximation 8(1992), 87–103.

    Article  MathSciNet  MATH  Google Scholar 

  5. A. F. Timan, Approximation of real-valued functions, in Russian, GIFMAT, 1960.

  6. J. L. Walsh, Interpolation and approximation by rational functions in the complex plane, AMS Colloquium Publications, Volume XX, 1960.

  7. J. L. Walsh, Overconvergence, degree of convergence and zeros of sequences of analytic functions, Duke Math. J. 13(1946), 195–235.

    Article  MathSciNet  MATH  Google Scholar 

  8. R. K. Kovacheva, On rational Chebyshev approximants to a real-valued function, Topics in polynomials of one and several variables and their applications, Ed. H. M. Srivastava and A. Vanushauskas, 1991, World Scientific Publ. Co

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Authors and Affiliations

  1. Chair of Solid State Physics, University of Lodz, Pomorska 149/153, P1-90-236, Lodz

    Julian Lawrynowicz

  2. Institute of Mathematics, Bulgarian Academy of Sciences, Acad. Bonchev str.8,13, Sofia, Bulgaria

    Ralitza K. Kovacheva

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  1. Julian Lawrynowicz
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  2. Ralitza K. Kovacheva
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Lawrynowicz, J., Kovacheva, R.K. Rational functions of best L p- approximation and analytic continuability. Results. Math. 43, 156–162 (2003). https://doi.org/10.1007/BF03322731

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  • DOI: https://doi.org/10.1007/BF03322731

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