Geodesic
On the Density of Compactly Supported Functions in a Space with Multiweighted Derivatives
Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 188-202.

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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.
Keywords: weight function, multiweighted derivative, space with multiweighted derivatives, closure of the set of compactly supported functions, density. 
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A. A. Kalybay; Zh. A. Keulimzhayeva; R. Oinarov. On the Density of Compactly Supported Functions in a Space with Multiweighted Derivatives. Informatics and Automation, Function Spaces, Approximation Theory, and Related Problems of Analysis, Tome 312 (2021), pp. 188-202. http://geodesic.mathdoc.fr/item/TRSPY_2021_312_a9/

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