Abstract:
This article deals with the proofs of some multidimensional Tauberian comparison theorems for generalized functions with supports in homogeneous cones, in particular, for measures and functions whose Laplace transforms have nonnegative imaginary parts. “Admissible” generalized functions, which can be regarded as multidimensional analogues of the so-called R-O-functions of Karamata, serve as comparison functions in these theorems. For circular and n-faced cones a criterion is obtained for admissibility which generalizes the well-known Keldysh Tauberian condition to the multidimensional case.
Bibliography: 9 titles.
Citation:
Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Tuberian comparison theorems for generalized functions in cones”, Math. USSR-Sb., 54:2 (1986), 499–524
This publication is cited in the following 8 articles:
Yu. N. Drozhzhinov, B. I. Zavialov, “Comparison Tauberian theorems and hyperbolic operators with constant coefficients”, Ufa Math. J., 7:3 (2015), 47–53
A. L. Yakymiv, “Admissible Functions for the Positive Octant”, Math. Notes, 76:3 (2004), 432–437
A. F. Grishin, I. V. Poedintseva, “Towards the Tauberian theorem of Keldysh”, J. Math. Sci. (N. Y.), 134:4 (2006), 2272–2287
A. L. Yakymiv, “Tauberian theorems and asymptotics of infinitely divisible
distributions in a cone”, Theory Probab. Appl., 48:3 (2004), 493–505
Yu. N. Drozhzhinov, B. I. Zavialov, “Multidimensional Abelian and Tauberian comparison theorems”, Math. USSR-Sb., 68:1 (1991), 85–110
B. I. Zavialov, “On the asymptotic properties of functions holomorphic in tubular cones”, Math. USSR-Sb., 64:1 (1989), 97–113
A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371
Zavialov B., “On the Asymptotic Properties of Functions Holomorphic in Tubular Cones”, 294, no. 5, 1987, 1048–1050
Citation in format AMSBIB
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