Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-26T03:07:10.006Z Has data issue: false hasContentIssue false
  • English
  • Français

Geometric Characterization of Interpolating Varieties for the (FN)-Space A0p of Entire Functions

Published online by Cambridge University Press:  20 November 2018

Carlos A. Berenstein ,
Bao Qin Li  and
Alekos Vidras
Carlos A. Berenstein
Affiliation:
Department of Mathematics University of Maryland College Park, Maryland 20742 U.S.A.
Bao Qin Li
Affiliation:
Department of Mathematics University of Maryland College Park, Maryland 20742 U.S.A.
Alekos Vidras
Affiliation:
Department of Mathematics University of Maryland College Park, Maryland 20742 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

A necessary and sufficient geometric characterization and a necessary and sufficient analytic characterization of interpolating varieties for the space of entire functions will be obtained in the paper, which as an application will also give a generalization of the well-known Pólya-Levinson density theorem.

Keywords

30D2030E05
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 1 , 01 February 1995 , pp. 28 - 43
Copyright
Copyright © Canadian Mathematical Society 1995

References

[BG] Berenstein, C.A. and Gay, G., Complex variables, an introduction, Springer Verlag, New York, 1991.Google Scholar
[BKS] Berenstein, C.A., Kawai, T. and Struppa, D.C., Interpolation theorems in several complex variables, Publ. Res. Inst. Math. Sci., Kyoto Univ. 846(1991), 1–13.Google Scholar
[BL1] Berenstein, C.A. and Li, Bao Qin, Interpolating varieties for spaces of me romorphic functions, J. Geom. Anal., to appear.Google Scholar
[BL2] Berenstein, C.A., Interpolation problems with growth conditions for entire functions in one and several complex variables, preprint, 1993.Google Scholar
[BL3] Berenstein, C.A., Interpolating varieties for weighted spaces of entire functions in Cn, Publicacions Mathématiques, 1993. to appear.Google Scholar
[BMT] Braun, R.W., Meise, R. and Taylor, B.A., Ultradifferentiable functions and Fourier analysis, Resultate Math. 17(1990), 206–223.Google Scholar
[BT] Berenstein, C.A. and Taylor, B.A., A new look at interpolation theory for entire functions of one variable, Adv. in Math. 33(1979), 109–143.Google Scholar
[GR] Grishin, A.F. and Russakovskii, A.M., Free interpolation by entire functions, Teor. Funktsiĭ Funktsional. Anal, i Prilozhen. 44(1985), 32–42.Google Scholar
[H] Horvath, J., Topological Vector Spaces, Addisson-Wesley, Massachusetts, 1963.Google Scholar
[L] Levinson, N., Gap and Density Theorems, Amer. Math. Soc, New York, 1940.Google Scholar
[Le] Levin, B.J., Distribution of Zeros of Entire Functions, Amer. Math. Soc, Providence, Rhode Island, 1964.Google Scholar
[MT] Meise, R. and Taylor, B.A., Sequence space representations for (FN)-algebras of entire functions modulo closed ideals, Studia Math. LXXXV(1987), 203–227.Google Scholar
[S] Schaefer, H.H., Topological Vector Spaces, The Macmillan Company, New York, 1966.Google Scholar
[SI] Squires, W.A., Necessary conditions for universal interpolation in , Canad. J. Math XXXIII(1981), 1356–1364.Google Scholar
[S2] Squires, W.A., Geometric conditions for universal interpolation in , Trans. Amer. Math. Soc. 280(1983), 401- 413.Google Scholar
[V] Vidras, A., Ph.D.dissertation, University of Maryland, 1992.Google Scholar