Laplace Transforms of Hyperfunctions: Another Foundation of the Heaviside Operational Calculus

Hikosaburo Komatsu
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Hikosaburo Komatsu: University of Tokyo, Department of Mathematics Faculty of Science

A chapter in Generalized Functions, Convergence Structures, and Their Applications, 1988, pp 57-70 from Springer

Abstract: Abstract The Laplace transform 1 $${\rm{\hat f}}\left( \lambda \right) = \int\limits_0^\infty {{\rm{e}}^{ - \lambda {\rm{x}}} {\rm{f}}\left( {\rm{x}} \right){\rm{dx}}}$$ is usually defined for a measurable function f(x) on [0,∞ ) satisfying the exponential type condition 2 $$\left| {{\rm{f}}\left( {\rm{x}} \right)} \right| \mathop 0,$$ with constants C and H. Then $${\rm{\hat f}}$$ (λ) is a holomorphic function on the half plane Re λ > H and satisfies the estimates $$\left| {{\rm{f}}\left( \lambda \right)} \right| \mathop

Keywords: Holomorphic Function; Entire Function; Exponential Type; Inversion Formula; Subharmonic Function (search for similar items in EconPapers)
Date: 1988
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DOI: 10.1007/978-1-4613-1055-6_5

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