publication . Article . 2011

Convolution of Distribution-Valued Functions. Applications.

Christian Bargetz;
  • Published: 15 Jun 2011
Abstract
In this article we examine products and convolutions of vector-valued functions. For nuclear normal spaces of distributions Proposition 25 in [31,p. 120] yields a vector-valued product or convolution if there is a continuous product or convolution mapping in the range of the vector-valued functions. For specific spaces, we generalize this result to hypocontinuous bilinear maps at the expense of generality with respect to the function space. We consider holomorphic, meromorphic and differentiable vector-valued functions and state propositions that contain assertions on products and convolutions of distribution-valued functions in literature as particular cases. M...
Subjects
free text keywords: Distributions, Convolution, Multiplication, Distribuciones, convolución, multiplicación
Related Organizations
32 references, page 1 of 3

[1] Jose Bonet, Leonhard Frerick, and Enrique Jorda, Extension of VectorValued Holomorphic and Harmonic Functions, Studia Math. 183 (2007), no. 3, 225{248.

[2] Jose Bonet, Enrique Jorda, and Manuel Maestre, Vector-Valued Meromorphic Functions, Arch. Math. (Basel) 79 (2002), no. 5, 353{359.

[3] N. Bourbaki, Elements de mathematique. Fasc. XXXIII. Varietes di erentielles et analytiques. Fascicule de resultats (Paragraphes 1 a 7), Actualites Scienti ques et Industrielles, No. 1333, Hermann et Cie., Paris, France, 1967 (fr).

[4] , Topological Vector Spaces. Chapters 1{5, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, Germany, 1987, Translated from the French by H. G. Eggleston and S. Madan.

[5] Peter Dierolf and Susanne Dierolf, Topological Properties of the Dual Pair hB( )0; B( )00i, Paci c J. Math. 108 (1983), no. 1, 51{82.

[6] Peter Dierolf and Jurgen Voigt, Convolution and S0-Convolution of Distributions, Collect. Math. 29 (1978), no. 3, 185{196.

[7] K. G. Grosse-Erdmann, A Weak Criterion for Vector-Valued Holomorphy, Math. Proc. Cambridge Philos. Soc. 136 (2004), no. 2, 399{411.

[8] Karl Goswin Grosse-Erdmann, The Locally Convex Topology on the Space of Meromorphic Functions, J. Austral. Math. Soc. Ser. A 59 (1995), no. 3, 287{303.

[9] Alexandre Grothendieck, Sur certains espaces de fonctions holomorphes. I, J. Reine Angew. Math. 192 (1953), 35{64 (fr).

[10] [11] , Sur certains espaces de fonctions holomorphes. II, J. Reine Angew. Math. 192 (1953), 77{95 (fr). , Produits tensoriels topologiques et espaces nucleaires, Mem. Amer.

Math. Soc. 1955 (1955), no. 16, Chap. I, 196, Chap. II, 140 (fr).

[12] Jean Horvath, Convolution de noyaux hypersinguliers, Initiation Seminar on Analysis: G. Choquet-M. Rogalski-J. Saint-Raymond, 19th Year: 1979/1980.

[13] , Sur la convolution des distributions, Bull. Sci. Math. (2) 98 (1974), no. 3, 183{192 (fr).

[14] John Horvath, Topological Vector Spaces and Distributions. Vol. I, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1966.

[15] , Composition of Hypersingular Integral Operators, Applicable Anal. 7 (1977), no. 3, 171{190.

32 references, page 1 of 3
Powered by OpenAIRE Open Research Graph
Any information missing or wrong?Report an Issue
publication . Article . 2011

Convolution of Distribution-Valued Functions. Applications.

Christian Bargetz;