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Abstract
In this paper we consider the problem of analytic continuation of analytic function on a strip domain, where the data are given only on the real axis. This is an ill-posed problem. The occurrence of its ill-posedness is intrinsically due to the high-frequency perturbation of data. However, Meyer wavelet has compact support in the frequency space. By expanding the data and the solution in a basis of Meyer wavelets, high-frequency components can be filtered away, and the Hölder-type stability estimates for both a priori and a posteriori choice rules are obtained. Numerical illustrations show that the method works effectively.
Acknowledgements
We are indebted to the anonymous referees for suggestions that helped us to improve the paper considerably. The work is supported by the National Natural Science Foundation of China (Nos. 11126187, 11171136, 61373174, 11326218), the Fundamental Research Funds for the Central Universities (Nos. K50511700002, K5051370013) and the China Postdoctoral Science Foundation (No. 2012M521742).