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A weighted estimate of best approximations in L2(Ω)
Yu. K. Dem'yanovich Leningrad State University
Abstract:
The best approximation ˜f [in the space L2(Ω)] of a function f, satisfying a Lipschitz condition with exponent α, 0⩽α⩽1, with the aid of certain spaces of local functions, dependent on a parameter h, is discussed. We obtain the estimate
‖
where
\|u\|_\beta=\max_{x\in\overline\Omega}|r^\beta u(x)|,\quad\beta\ge0\quad u\in C(\overline\Omega)
and r=r(x) is the distance of the point x from the boundary of the domain \Omega.
Received: 12.01.1976
Citation:
Yu. K. Dem'yanovich, “A weighted estimate of best approximations in L_2(\Omega)”, Mat. Zametki, 22:2 (1977), 245–255; Math. Notes, 22:2 (1977), 627–633
Linking options:
https://www.mathnet.ru/eng/mzm8045 https://www.mathnet.ru/eng/mzm/v22/i2/p245
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Abstract page: | 180 | Full-text PDF : | 69 | First page: | 1 |
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