A remark concerning Pincherle bases |
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Authors: | N I Nagnibida |
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Institution: | 1. Chernovitskii State University, USSR
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Abstract: | In this note we find sufficient conditions for uniqueness of expansion of any two functionsf(z) and g(z) which are analytic in the circle ¦ z ¦ < R (0 < R <∞) in series $$f(z) = \sum\nolimits_{n = 0}^\infty {(a_n f_2 (z) + b_n g_n (z))}$$ and $$g_i (z) = \sum\nolimits_{n = 0}^\infty {a_n \lambda _n f_n (z)} + b_n \mu _n f_n (x)),$$ which are convergent in the compact topology, where (f n {z} n=0 ∞ and {g} n=0 ∞ are given sequences of functions which are analytic in the same circle while {λ n } n=0 ∞ and {μ n } n=0 ∞ are fixed sequences of complex numbers. The assertion obtained here complements a previously known result of M. G. Khaplanov and Kh. R. Rakhmatov. |
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