On the Density of Compactly Supported Functions in a Space with Multiweighted Derivatives
Kalybay A.A. Keulimzhayeva Z.A. Oinarov R.
March 2021Pleiades journals
Proceedings of the Steklov Institute of Mathematics
2021#312Issue 1179 - 193 pp.
Abstract: We define a space with multiweighted derivatives on the half-axis. A multiweighted derivative of a function is an operation under which each subsequent derivative is taken of the function multiplied by some weight function. All weight functions involved in the definition of a multiweighted derivative are assumed to be sufficiently smooth; therefore, the set of compactly supported infinitely smooth functions belongs to the space with multiweighted derivatives, and the closure of this set in the norm of the space is a subspace of the latter. We study the mutual relation between these spaces depending on the integral behavior of the weight functions in the neighborhood of zero and infinity.
closure of the set of compactly supported functions , density , multiweighted derivative , space with multiweighted derivatives , weight function
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L. N. Gumilyov Eurasian National University, Satpayev Str. 2, Nur-Sultan, 010008, Kazakhstan
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