Functiones et Approximatio Commentarii Mathematici

On the Laplace transform for vector valued hyperfunctions

Paweł Domański and Michael Langenbruch

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Abstract

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

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

Dates
First available in Project Euclid: 9 December 2010

Permanent link to this document
https://projecteuclid.org/euclid.facm/1291903394

Digital Object Identifier
doi:10.7169/facm/1291903394

Mathematical Reviews number (MathSciNet)
MR2767167

Zentralblatt MATH identifier
1206.44001

Subjects
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.)

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

Citation

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. https://projecteuclid.org/euclid.facm/1291903394


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References

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