This article is cited in 3 scientific papers (total in 3 papers)
A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the positive octant
Yu. N. Drozhzhinov, B. I. Zavialov
Steklov Mathematical Institute, Russian Academy of Sciences
The paper is devoted to a multidimensional Tauberian theorem of Hardy–Littlewood type for quasiasymptotic expansions of measures concentrated in the positive octant. Here the quasiasymptotic expansion is assumed to be local, i.e., its terms are generalized functions concentrated at the origin. The asymptotic behavior of the remainder is estimated with respect to the scale of regularly varying (self-similar) functions along trajectories defined by one-parameter groups of automorphisms of the cone in which the measure is concentrated. The case of one variable is investigated in more detail; in particular, a Hardy–Littlewood type theorem is proved for generalized functions that are nonnegative measures for large values of the argument.
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Russian Academy of Sciences. Sbornik. Mathematics, 1995, 81:1, 185–209
MSC: Primary 28A35, 40E05; Secondary 46F12
Yu. N. Drozhzhinov, B. I. Zavialov, “A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the positive octant”, Mat. Sb., 185:2 (1994), 57–86; Russian Acad. Sci. Sb. Math., 81:1 (1995), 185–209
Citation in format AMSBIB
\by Yu.~N.~Drozhzhinov, B.~I.~Zavialov
\paper A Tauberian theorem for quasiasymptotic decompositions of measures with supports in the~positive octant
\jour Mat. Sb.
\jour Russian Acad. Sci. Sb. Math.
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Yu. N. Drozhzhinov, B. I. Zavialov, “Theorems of Hardy–Littlewood type for signed measures on a cone”, Sb. Math., 186:5 (1995), 675–693
A. L. Yakymiv, “A Tauberian theorem for multiple power series”, Sb. Math., 207:2 (2016), 286–313
Yu. N. Drozhzhinov, “Multidimensional Tauberian theorems for generalized functions”, Russian Math. Surveys, 71:6 (2016), 1081–1134
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