ON THE INVERSION OF THE CONVOLUTION AND LAPLACE TRANSFORM

@inproceedings{Baeumer2002ONTI,
  title={ON THE INVERSION OF THE CONVOLUTION AND LAPLACE TRANSFORM},
  author={Boris Baeumer},
  year={2002}
}
We present a new inversion formula for the classical, finite, and asymptotic Laplace transform f̂ of continuous or generalized functions f . The inversion is given as a limit of a sequence of finite linear combinations of exponential functions whose construction requires only the values of f̂ evaluated on a Müntz set of real numbers. The inversion sequence converges in the strongest possible sense. The limit is uniform if f is continuous, it is in L1 if f ∈ L1, and converges in an appropriate… CONTINUE READING

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Showing 1-10 of 13 references

Dissertation

Baeumer, B. A Vector-Valued Operational Calculus, Abstract Cauchy Problems
Louisiana State University, • 1997
View 5 Excerpts
Highly Influenced

On the Foiaş theorem on convolution of continuous functions

K. Skórnik
Asymptotic Laplace transforms and evolution equations . Evolution equations , Feshbach resonances , singular Hodge theory • 1999

operator theory

B. Bäumer, G. Lumer, F. Neubrander. Convolution kernels, generalized functions. Generalized functions
and dynamical systems (Brussels, 1997), 68–78, Res. Notes Math. 399, Chapman & Hall/CRC, Boca Raton, FL, • 1999
View 2 Excerpts

singular Hodge theory

G. Lumer, F. Neubrander. Asymptotic Laplace transforms, evolution equations. Evolution equations, Feshbach resonances
37–57, Math. Top. 16, Wiley-VCH, Berlin, • 1999
View 2 Excerpts

Conferenze del Seminario di Matematica dell’Universitá di Bari

B. Bäumer, F. Neubrander. Laplace transform methods for evolutio equations
259, 27-60, • 1994
View 1 Excerpt

1-2

Mikusiński, J. Operational Calculus. v
Pergamon Press, 2nd edition, • 1987
View 3 Excerpts

Complex Analysis and Applications ’85 (Varna

Skórnik, K. On the Foiaş theorem on convolution of continuous functions
1985), 604–608, Publ. House Bulgar. Acad. Sci., Sofia, • 1986

Approximation des opérateurs de J . Mikusiński par des fonctions continues

G. Lumer
Studia Mathematica • 1961

Studia Mathematica 21

Foiaş, C. Approximation des opérateurs de J. Mikusiński par continues
73–74, • 1961
View 1 Excerpt