Many-dimensional operators of convolution type in spaces of weight-integrable functions

V. S. Rabinovich

doi:10.1007/BF01105582

Many-dimensional operators of convolution type in spaces of weight-integrable functions

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Abstract

We show that a convolution operator in the weight space L_p is similar to a generalized convolution operator in L_p. We obtain necessary and sufficient conditions for an operator of convolution type, acting in a weight space, to have the Noether property in a cone. These conditions say, in effect, that the operator symbol must not degenerate on the hull of some tubular domain associated with the weight and the cone.

Original language	English
Pages (from-to)	747-752
Number of pages	6
Journal	Mathematical Notes of the Academy of Sciences of the USSR
Volume	16
Issue number	2
DOIs	https://doi.org/10.1007/BF01105582
State	Published - Aug 1974
Externally published	Yes

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AB - We show that a convolution operator in the weight space Lp is similar to a generalized convolution operator in Lp. We obtain necessary and sufficient conditions for an operator of convolution type, acting in a weight space, to have the Noether property in a cone. These conditions say, in effect, that the operator symbol must not degenerate on the hull of some tubular domain associated with the weight and the cone.

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M3 - Artículo

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Many-dimensional operators of convolution type in spaces of weight-integrable functions

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