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Интеллектуальная Система Тематического Исследования НАукометрических данных |
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We consuder the spectral properties of a singular string with a self-similar (fractal) mass distribution. As problems related to this equation, a brief introduction to the theory of affine self-similar functions will be given. Their application to spectral problems will be disclosed. The second direction related to the string equation with a weight-distribution is the theory of embeddings in Sobolev spaces. Exact embedding constants will be discussed. It is also planned to discuss the connection between the problem of exact estimates of intermediate derivatives in Sobolev spaces and approximation theory in L_p spaces.