×
Drozhzhinov, Yu. N.; Zav’yalov, B. I.

Asymptotically homogeneous generalized functions at zero and convolution equations with kernels quasi-homogeneous polynomial symbols. (English. Russian original) Zbl 1186.46040

Dokl. Math. 79, No. 3, 356-359 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 3, 300-303 (2009).
Asymptotically homogeneous functions have some interesting properties and are involved in many Tauberian theorems as well as the problems in mathematical physics. In this paper, the authors give a similar description of asymptotically quasi-homogeneous generalized functions at zero. The results are also applied in order to construct asymptotically homogeneous solutions of differential equations which are similar to the quasi-homogeneous case.
Reviewer: Adem Kilicman (Serdang Selangor)

Cited in 6 Documents

MSC:

46F10 Operations with distributions and generalized functions
35G20 Nonlinear higher-order PDEs
46F05 Topological linear spaces of test functions, distributions and ultradistributions

Keywords:

convolution equations; kernels; quasi-homogeneous polynomial; asymptotically homogeneous generalised functions
Cite Review PDF
Full Text: DOI

References:

[1] Yu. N. Drozhzhinov and B. I. Zav’yalov, Izv. Akad. Nauk, Ser. Mat. 70(6), 45–92 (2006). · doi:10.4213/im866
[2] Yu. N. Drozhzhinov and B. I. Zav’yalov, Dokl. Math. 78, 503–507 (2008) [Dokl. Akad. Nauk 421, 157–161 (2008)]. · Zbl 1246.46042 · doi:10.1134/S1064562408040091
[3] V. S. Vladimirov, Yu. N. Drozhzhinov, and B. I. Zav’yalov, Multidimensional Tauberian Theorems for Distributions (Nauka, Moscow, 1986) [in Russian].
[4] E. Seneta, Regularly Varying Functions (Springer-Verlag, Berlin, 1976; Nauka, Moscow, 1985). · Zbl 0324.26002
[5] O. Grudzinski, Quasi-homogeneous Distributions (North-Holland, Amsterdam, 1991).
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.