Convolution equations on spaces of quasi-nuclear functions of a given type and order. (English) Zbl 1211.46038

This nice paper is a kind of continuation of the author’s paper [Port. Math. (N. S.) 65, No. 2, 285–309 (2008; Zbl 1152.46033)]. The author proves existence and approximation results for convolution equations on the spaces of \((s;(r,q))\)-quasi-nuclear mappings of a given type and order on a Banach space \(E\). The results of the paper generalize previous works of C. Gupta, B. Malgrange, M. C. Matos and A. Martineau [Bull. Soc. Math. Fr. 95, 109–154 (1967; Zbl 0167.44202)] related to partial differential equations with constant coefficients for entire functions.


46G25 (Spaces of) multilinear mappings, polynomials
46G20 Infinite-dimensional holomorphy
46N20 Applications of functional analysis to differential and integral equations
Full Text: Euclid