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

Fávaro, Vinícius V.

Bull. Belg. Math. Soc. - Simon Stevin 17, No. 3, 535-569 (2010).

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.

Reviewer: Daniel Pellegrino (João Pessoa)

MSC:

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

Keywords:

convolution equations; partial differential equations; Banach spaces; homogeneous polynomials; division theorems; quasi-nuclear mappings

Citations:

Zbl 0167.44202; Zbl 1152.46033