On the Laplace transform for vector valued hyperfunctions
Domański, Paweł ; Langenbruch, Michael
Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, p. 129-159 / Harvested from Project Euclid
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We introduce a Laplace transform for Laplace hyperfunctions valued in a complete locally convex space $X$. In this general case the Laplace transform is a compatible family of holomorphic functions with values in local Banach spaces. Especially interesting is the case where $X=L_b(E,F)$ is the space of operators between locally convex spaces. In the forthcoming paper [6] this will be applied to solve the abstract Cauchy problem for operators in complete ultrabornological locally convex spaces (like spaces of smooth functions and distributions) extending results of Komatsu for operators in Banach spaces.
Publié le : 2010-12-15
Classification:  Abstract Cauchy problem,  Laplace hyperfunctions,  Laplace distributions,,  Laplace transform,,  Laplace inversion formula,  exponential growth.,  44A10,  46F15,  32A45,  47B37 
@article{1291903394,
     author = {Doma\'nski, Pawe\l\ and Langenbruch, Michael},
     title = {On the Laplace transform for vector valued hyperfunctions},
     journal = {Funct. Approx. Comment. Math.},
     volume = {42},
     number = {1},
     year = {2010},
     pages = { 129-159},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1291903394}
}

Domański, Paweł; Langenbruch, Michael. On the Laplace transform for vector valued hyperfunctions. Funct. Approx. Comment. Math., Tome 42 (2010) no. 1, pp.  129-159. http://gdmltest.u-ga.fr/item/1291903394/