The range of the restriction map for a multiplicity variety in Hörmander algebras of entire functions

The final publication is available at Springer via http://dx.doi.org/10.1007/s00009-013-0318-5[EN] Characterizations of interpolating multiplicity varieties for Hörmander algebras Ap(C) and A0 p(C) of entire functions were obtained by Berenstein and Li (J Geom Anal 5(1):1–48, 1995) and Berenstein et al. (Can J Math 47(1):28–43, 1995) for a radial subharmonic weight p with the doubling property. In this note we consider the case when the multiplicity variety is not interpolating, we compare the range of the associated restriction map for two weights q ≤ p and investigate when the range of the restriction map on Ap(C) or A0 p(C) contains certain subspaces associated in a natural way with the smaller weight q.This research was partially supported by MEC and FEDER Project MTM2010-15200.Bonet Solves, JA.; Fernandez Rosell, C. (2014). The range of the restriction map for a multiplicity variety in Hörmander algebras of entire functions. Mediterranean Journal of Mathematics. 11(2):643-652. https://doi.org/10.1007/s00009-013-0318-5643652112Berenstein, C.A., Gay, R.: Complex variables. An Introduction. Graduate Texts in Mathematics, vol. 125. Springer, New York (1991)Berenstein, C.A., Gay R.: Complex Analysis and Special Topics in Harmonic Analysis. Springer, New York (1995)Berenstein C.A., Li B.Q.: Interpolating varieties for spaces of meromorphic functions. J. Geom. Anal. 5(1), 1–48 (1995)Berenstein C.A., Li B.Q., Vidras A.: Geometric characterization of interpolating varieties for the (FN)-space $${A^{0}_p}$$ of entire functions. Can. J. Math. 47(1), 28–43 (1995)Berenstein C.A., Taylor B.A.: A new look at interpolation theory for entire functions of one variable. Adv. Math. 33(2), 109–143 (1979)Bonet J., Galbis A.: The range of non-surjective convolution operators on Beurling spaces. Glasg. Math. J. 38(1), 125–135 (1996)Bonet J., Galbis A., Momm S.: Nonradial Hörmander algebras of several variables and convolution operators. Trans. Am. Math. Soc. 353(6), 2275–2291 (2001)Braun R.W.: Weighted algebras of entire functions in which each closed ideal admits two algebraic generators. Mich. Math. J. 34(3), 441–450 (1987)Braun R.W., Meise R., Taylor B.A.: Ultradifferentiable functions and Fourier analysis. Results Math. 17(3–4), 206–237 (1990)Buckley J., Massaneda X., Ortega-Cerdà J.: Traces of functions in Fock spaces on lattices of critical density. Bull. Lond. Math. Soc. 44(2), 222–240 (2012)Hartmann A., Massaneda X.: On interpolating varieties for weighted spaces of entire functions. J. Geom. Anal. 10(4), 683–696 (2000)Massaneda X., Ortega-Cerdà J., Ounaïes M.: A geometric characterization of interpolation in $${\hat{\mathcal{E}}'(\mathbb{R})}$$ . Trans. Am. Math. Soc. 358, 3459–3472 (2006)Massaneda, X., Ortega-Cerdà, J., Ounaïes, M.: Traces of Hörmander algebras on discrete sequences. In: Analysis and mathematical physics. Trends in Mathematics, pp. 397–408. Birkhäuser, Basel (2009)Meise R.: Sequence space representations for (DFN)-algebras of entire functions modulo closed ideals. J. Reine Angew. Math. 363, 59–95 (1985)Meise R., Taylor B.A.: Sequence space representations for (FN)-algebras of entire functions modulo closed ideals. Studia Math. 85(3), 203–227 (1987)Meise, R., Vogt, D.: Introduction to functional analysis. Oxford Graduate Texts in Mathematics, vol. 2. The Clarendon Press Oxford University Press, New York (1997). Translated from the German by M. S. Ramanujan and revised by the authorsOunaïes M.: Geometric conditions for interpolation in weighted spaces of entire functions. J. Geom. Anal. 17(4), 701–715 (2007)Ounaïes M.: Interpolation by entire functions with growth conditions. Mich. Math. J. 56(1), 155–171 (2008)Ounaïes, M.: Interpolation dans les algèbres de Hörmander. Université Louis Pasteur. Institut de Recherche Mathématique Avancée (IRMA), Strasbourg (2008)Stromberg, K.R.: Introduction to classical real analysis. Wadsworth International, Belmont, California. Wadsworth International Mathematics Series (1981)Zioło P.: Geometric characterization of interpolation in the space of Fourier-Laplace transforms of ultradistributions of Roumieu type. Collect. Math. 62(2), 161–172 (2011