Interpolation of Functions with Zero Spherical Averages Obeying Growth Constraints

Let , with and , be the set of locally integrable functions with the zero integrals over all balls of radius in . We study the interpolation problem , with , for functions in with growth constraints at infinity. Under consideration is the case that is a set of points on a certain straight line in wh...

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Bibliographic Details
Published in:Siberian mathematical journal 2024-09, Vol.65 (5), p.1043-1052
Main Authors: Volchkov, V. V., Volchkov, Vit. V.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Let , with and , be the set of locally integrable functions with the zero integrals over all balls of radius in . We study the interpolation problem , with , for functions in with growth constraints at infinity. Under consideration is the case that is a set of points on a certain straight line in which is close in some sense to a finite union of arithmetic progressions and is a sequence of complex numbers satisfying the condition . We show that this interpolation problem is solvable in the class of those functions in which, together with their derivatives, satisfy a special decay condition at infinity. The condition is an upper bound that implies power decay in the directions orthogonal to and also cannot be significantly improved along the straight line  .
ISSN:0037-4466
1573-9260
DOI:10.1134/S0037446624050069