The Hadamard multiplication theorem in several complex variables

References

• Render H. Hadamard’s multiplication theorem -- recent developments. Coll. Math. 1997;74:79–92.
   Google Scholar
• Bernal-Gonzalez L, Calderon-Moreno MC, Prado-Bassas JA. Cyclicity of coefficient multipliers: linear structure. Acta Math. Hung. 2007;114:287–300.
   Web of Science ®Google Scholar
• Brück R, Müller J. Invertible elements in a convolution algebra of holomorphic functions. Math. Ann. 1992;294:421–438.
   Web of Science ®Google Scholar
• Brück R, Müller J. Closed ideals in a convolution algebra of holomorphic fucntions. Can. J. Math. 1995;47:915–928.
   Web of Science ®Google Scholar
• Brück R, Render H. Invertibility of holomorphic functions with respect to the Hadamard product. Complex Var. 2000;42:207–223.
   Google Scholar
• Grosse-Erdmann K-G. On the Borel-Okada theorem and the Hadamard multiplication theorem. Complex Var. 1993;22:101–112.
   Google Scholar
• Müller J. The Hadamard multiplication theorem and applications in summability theory. Complex Var. 1992;18:155–166.
   Google Scholar
• Müller J. Coefficient multipliers from H(G1) into H(G2). Arch. Math. 1993;61:75–81.
   Web of Science ®Google Scholar
• Müller J, Naik S, Ponnusany S. Growth of entire functions of exponential type defined by convolution. Arch. Math. 2006;87:330–342.
   Web of Science ®Google Scholar
• Müller J, Pohlen T. The Hadamard product as a universality preserving operator. Comput. Methods Funct. Theor. 2010;10:281–289.
   Web of Science ®Google Scholar
• Müller J, Pohlen T. The Hadamard product on open sets in the extended plane. Complex Anal. Oper. Theor. 2012;6:257–274.
   Web of Science ®Google Scholar
• Render H, Sauer A. Algebras of holomorphic Fucntions with Hadamard multiplication. Studia Math. 1996;118:77–101.
   Web of Science ®Google Scholar
• Render H. Homomorphisms on Hadamard algebras. Rend. Circ. Mat. Palermo, Serie II. Suppl. 40. 1996:153–158.
   Google Scholar
• Render H, Sauer A. Invariance properties of homeomorphisms on algebras of holomorphic functions with the Hadamard product. Studia Math. 1996;121:53–65.
   Web of Science ®Google Scholar
• Domański P, Langenbruch M. Representation of multipliers on spaces of real analytic functions. Analysis. 2012;32:137–162.
   Google Scholar
• Domański P, Langenbruch M. Algebra of multipliers on the space of real analytic functions of one variable. Studia Math. 2012;212:155–171.
   Web of Science ®Google Scholar
• Domański P, Langenbruch M. Hadamard multipliers on spaces of real analytic functions. Adv. Math. 2013;240:575–612.
   Web of Science ®Google Scholar
• Doma{\’n}ski P, Langenbruch M. Euler type partial differential operators on real analytic functions. J. Math. Anal. Appl. doi:10.1016/j.jmaa.2016.05.018.
   Web of Science ®Google Scholar
• Doma{\’n}ski P, Langenbruch M. Interpolation of holomorphic functions and surjectivity of Taylor coefficient multipliers. Adv. Math. 2016;293:782–855.
   Web of Science ®Google Scholar
• Domański P, Langenbruch M, Vogt D. Hadamard type operators on spaces of real analytic functions in several variables. J. Funct. Anal. 2015;269:3868–3913.
   Web of Science ®Google Scholar
• Bieberbach L. Analytische Fortsetzung. Berlin: Springer; 1955.
   Google Scholar
• Hille E. Analytic function theory. Vol. II. Boston: Ginn and Co.; 1962.
   Google Scholar
• Stout EL. Polynomial convexity. Boston: Birkhäuser; 2007.
   Google Scholar
• Range RM. Holomorphic functions and integral representations in several complex variables. New York: Springer; 1986.
   Google Scholar
• Vladimirov VS. Methods of the theory of functions of many complex variables. New York: Dover Publications; 2007.
   Google Scholar
• Chen H, Luo Z, Zhang C. On a family of symmetric hypergeometric functions of several variables and their Euler type integral representation. Adv. Math. 2014;252:652–683.
   Web of Science ®Google Scholar
• Schaefer HH. Topological vector spaces. 2nd ed. New York: Springer; 1999.
   Google Scholar
• Hörmander L. An introduction to complex analysis in several variables. 3rd ed. Amsterdam: North-Holland Publishing Company; 1990.
   Google Scholar
• Hörmander L. Notions of convexity. Boston: Birkhäuser; 2007.
   Google Scholar
• Jarnicki M, Pflug P. First steps in several complex variables: Reinhardt domains. Zurich: European Mathematical Society Publishing House; 2008.
   Google Scholar