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.

MSC:

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

Citations:

Zbl 0167.44202; Zbl 1152.46033
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