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Growth and approximation of solutions to a class of certain linear partial differential equations in ℝN

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Mathematica Slovaca

Abstract

In this paper we consider the equation ∇2 φ + A(r 2)X · ∇φ + C(r 2)φ = 0 for X ∈ ℝN whose coefficients are entire functions of the variable r = |X|. Corresponding to a specified axially symmetric solution φ and set C n of (n + 1) circles, an axially symmetric solution Λ * n (x, η;C n ) and Λ n (x, η;C n ) are found that interpolates to φ(x, η) on the C n and converges uniformly to φ(x, η) on certain axially symmetric domains. The main results are the characterization of growth parameters order and type in terms of axially symmetric harmonic polynomial approximation errors and Lagrange polynomial interpolation errors using the method developed in [MARDEN, M.: Axisymmetric harmonic interpolation polynomials in ℝN, Trans. Amer. Math. Soc. 196 (1974), 385–402] and [MARDEN, M.: Value distribution of harmonic polynomials in several real variables, Trans. Amer. math. Soc. 159 (1971), 137–154].

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  1. Department of Mathematics, M.M.H. College, Model Town Ghaziabad, 201 001, U.P., India

    Devendra Kumar

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  1. Devendra Kumar
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Kumar, D. Growth and approximation of solutions to a class of certain linear partial differential equations in ℝN . Math. Slovaca 64, 139–154 (2014). https://doi.org/10.2478/s12175-013-0192-4

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  • DOI: https://doi.org/10.2478/s12175-013-0192-4

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