Functiones et Approximatio Commentarii Mathematici

On the Laplace transform for vector valued hyperfunctions

Paweł Domański and Michael Langenbruch

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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.

Article information

Funct. Approx. Comment. Math., Volume 43, Number 2 (2010), 129-159.

First available in Project Euclid: 9 December 2010

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 44A10: Laplace transform
Secondary: 46F15: Hyperfunctions, analytic functionals [See also 32A25, 32A45, 32C35, 58J15] 32A45: Hyperfunctions [See also 46F15] 47B37: Operators on special spaces (weighted shifts, operators on sequence spaces, etc.)

Abstract Cauchy problem Laplace hyperfunctions Laplace distributions, Laplace transform, Laplace inversion formula exponential growth.


Domański, Paweł; Langenbruch, Michael. On the Laplace transform for vector valued hyperfunctions. Funct. Approx. Comment. Math. 43 (2010), no. 2, 129--159. doi:10.7169/facm/1291903394.

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