Geodesic
Biharmonic wavelets and their applications
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 76-89

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We propose a solution method for the basic boundary value problem for biharmonic functions. In this method, a special system of functions is orthogonalized and Fourier series in this system are considered. It is proved that the constructed series converge inside the domain. Biharmonic wavelets are constructed based on the orthogonalized system. It is established that series of wavelets converge uniformly in the domain with boundary.
Keywords: biharmonic function, boundary value problem, wavelets. 
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     author = {G. A. Dubosarskii},
     title = {Biharmonic wavelets and their applications},
     journal = {Trudy Instituta matematiki i mehaniki},
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     publisher = {mathdoc},
     volume = {22},
     number = {3},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a7/}
}
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G. A. Dubosarskii. Biharmonic wavelets and their applications. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 22 (2016) no. 3, pp. 76-89. http://geodesic.mathdoc.fr/item/TIMM_2016_22_3_a7/