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Notes on interpolation. VI

On the stability of the interpolation on an infinite interval

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References

  1. E. Egerváry andP. Turán, Notes on interpolation. V,Acta Math. Acad. Sci. Hung.,9 (1958), pp. 259–267.

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  2. L. Fejér, Über Interpolation,Gött. Nachr., (1916), pp. 1–26.

  3. As Mr.J. Balázs remarked, one cannot replace 0 in the definition by\(\mathop {min}\limits_v (y_v - y_v^* )e^{ - x_{vn} } \) as the exampley v =e x vn ,y *v =0 (v=1, 2,...,n) shows at once. Analogous remark holds for Definition II.

  4. From our analysis it follows that for all realy v andy *v (i.e. not requiringy v ≧y *v ) the inequality holds forx≧0.

  5. Again we obtained for all realy v andy *v (i. e. not requiringy v ≧y *v ) the inequality for all real valuesx.

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Authors and Affiliations

  1. Budapest

    E. Egerváry & P. Turán (member of the Academy)

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  1. E. Egerváry
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  2. P. Turán
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Egerváry, E., Turán, P. Notes on interpolation. VI. Acta Mathematica Academiae Scientiarum Hungaricae 10, 55–62 (1959). https://doi.org/10.1007/BF02063289

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  • DOI: https://doi.org/10.1007/BF02063289

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