Tauberian theorems for generalized functions with values in Banach spaces

Izvestiya Mathematics

Volumn 66, Issue 4, 2002, Pages 701-769

  Drozhzhinov, Yu N ^a   Zav'yalov, B I ^a  

^a STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33748504600     PISSN: 10645632     EISSN: 14684810     Source Type: Journal    
DOI: 10.1070/IM2002v066n04ABEH000395     Document Type: Article

References (15)

1. Yu. N. Drozhzhinov and B. I. Zav'yalov, "Tauberian theorems for generalized multiplicative convolutions", Izv. Ross. Akad. Nauk Ser. Mat. 64:1 (2000), 37-94;
2. English transl., Izv. Math. 64 (2000), 35-92.
3. I. M. Gel'fand and G. E. Shilov, Generalized functions. Vol. I: Properties and operations, Fizmatgiz, Moscow 1959; English transl., Academic Press, New York-London 1964.
4. V. S. Vladimirov, Yu. N. Drozhzhinov and B. I. Zav'yalov, Tauberian theorems for generalized functions, Nauka, Moscow 1986; English transl., Kluwer, Dordrecht 1988.
5. E. Seneta, Regularly varying functions, Springer-Verlag, Berlin 1976; Russian transl., Nauka, Moscow 1985.
6. V. G. Maz'ya, Sobolev spaces, Izdat. Leningrad. Univ., Leningrad 1985; English transl., Springer-Verlag, Berlin 1985.
7. L. Hörmander, An introduction to complex analysis in several variables, Van Nostrand, Princeton, NJ 1966; Russian transl., Mir, Moscow 1968.
8. Yu. N. Drozhzhinov and B. I. Zav'yalov, "A Wiener-type Tauberian theorem for generalized functions of slow growth", Mat. Sb. 189:7 (1998), 91-130;
9. English transl., Sb. Math. 189 (1998), 1047-1086.
10. T. Muramatu, "On Besov spaces and Sobolev spaces of generalized functions defined on a general region", Publ. Res. Inst. Math. Sci. 9 (1974), 325-396.
11. J. B. Garnett, Bounded analytic functions, Academic Press, New York-London 1981; Russian transl., Mir, Moscow 1984.
12. K. Yosida, Functional analysis, Springer-Verlag, Berlin-Göttingen- Heidelberg 1965; Russian transl., Mir, Moscow 1967.
13. N. Dunford and J.-T. Schwartz, Linear operators. Part I: General theory, Interscience, New York-London 1958; Russian transl., Inostr. Lit., Moscow 1962.
14. O. V. Besov, V. P. Il'in and S. M. Nikol'skii, Integral representations of functions and imbedding theorems, 2nd ed., Nauka, Moscow 1996; English transl, of 1st ed., vols. I, II, John Wiley, New York 1978, 1979.
15. E. M. Stein, Singular integrals and differentiability properties of functions, Princeton Univ. Press, Princeton, NJ 1970; Russian transl., Mir, Moscow 1973.