Complementing the authors' earlier joint papers on the application of orthogonal wavelets to represent solutions of Dirichlet problems with the Laplace operator and its powers in a disk and a ring and of interpolating wavelets for the same problem in a disk, we develop a technique of applying periodic interpolating wavelets in a ring for the Dirichlet boundary value problem. The emphasis is not on the exact representation of the solution in the form of (double) series in a wavelet system but on the approximation of solutions with any given accuracy by finite linear combinations of dyadic rational translations of special harmonic polynomials; these combinations are constructed with the use of interpolating wavelets. The obtained approximation formulas are simply calculated, especially if the squared Fourier transform of the Meyer scaling function with the properties described in the paper is explicitly defined in terms of the corresponding elementary functions.

中文翻译：

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环形谐波插值小波

补充作者先前关于应用正交小波来表示用Laplace算子及其在磁盘和环中的幂的Dirichlet问题的解以及在磁盘中对同一问题的小波插值的联合论文，我们开发了一种应用Dirichlet边值问题在环中的周期内插小波。重点不是在小波系统中以（双）级数形式精确表示解，而是通过特殊调和多项式的有理有理平移的有限线性组合来逼近具有给定精度的解。这些组合是使用插值小波构造的。只需简单地计算出获得的近似公式，