A geometric characterization of interpolation in ℰ̂′(ℝ)

Massaneda, Xavier; Ortega-Cerdà, Joaquim; Ounaïes, Myriam

doi:10.1090/S0002-9947-05-03872-9

A geometric characterization of interpolation in $\hat {\mathcal {E}}^\prime (\mathbb {R})$
HTML articles powered by AMS MathViewer

by Xavier Massaneda, Joaquim Ortega-Cerdà and Myriam Ounaïes PDF

Trans. Amer. Math. Soc. 358 (2006), 3459-3472 Request permission

Abstract:

We give a geometric description of the interpolating varieties for the algebra of Fourier transforms of distributions (or Beurling ultradistributions) with compact support on the real line.

References

Göran Björck, Linear partial differential operators and generalized distributions, Ark. Mat. 6 (1966), 351–407 (1966). MR 203201, DOI 10.1007/BF02590963
Carlos A. Berenstein and Roger Gay, Complex analysis and special topics in harmonic analysis, Springer-Verlag, New York, 1995. MR 1344448, DOI 10.1007/978-1-4613-8445-8
Carlos A. Berenstein and Bao Qin Li, Interpolating varieties for spaces of meromorphic functions, J. Geom. Anal. 5 (1995), no. 1, 1–48. MR 1315656, DOI 10.1007/BF02926441
Léon Ehrenpreis and Paul Malliavin, Invertible operators and interpolation in $AU$ spaces, J. Math. Pures Appl. (9) 53 (1974), 165–182 (English, with French summary). MR 402497
John B. Garnett, Bounded analytic functions, Pure and Applied Mathematics, vol. 96, Academic Press, Inc. [Harcourt Brace Jovanovich, Publishers], New York-London, 1981. MR 628971
Lars Hörmander, Notions of convexity, Progress in Mathematics, vol. 127, Birkhäuser Boston, Inc., Boston, MA, 1994. MR 1301332
A. F. Leont′ev, Conditions for the expansion of analytic functions in Dirichlet series, Izv. Akad. Nauk SSSR Ser. Mat. 36 (1972), 1282–1295 (Russian). MR 0335763
Joaquim Ortega-Cerdà and Kristian Seip, Multipliers for entire functions and an interpolation problem of Beurling, J. Funct. Anal. 162 (1999), no. 2, 400–415. MR 1682065, DOI 10.1006/jfan.1998.3357
Myriam Ounaies, On interpolating discrete varieties for weighted spaces of entire functions, Anal. Math. 29 (2003), no. 1, 59–74 (English, with English and Russian summaries). MR 1965313, DOI 10.1023/A:1022850631287
W. A. Squires, Necessary conditions for universal interpolation in $\hat {\cal E}^{\prime }$, Canadian J. Math. 33 (1981), no. 6, 1356–1364. MR 645231, DOI 10.4153/CJM-1981-104-9
William A. Squires, Geometric condition for universal interpolation in $\hat {\cal E}^{\prime }$, Trans. Amer. Math. Soc. 280 (1983), no. 1, 401–413. MR 712268, DOI 10.1090/S0002-9947-1983-0712268-7