On the inversion of the convolution and Laplace transform

Transactions of the American Mathematical Society

Volumn 355, Issue 3, 2003, Pages 1201-1212

  Baeumer, Boris ^a  

^a UNIVERSITY OF OTAGO   (New Zealand)

Author keywords

Generalized functions; Integral transforms; Operational calculus

Indexed keywords

EID: 0037343416     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-02-03174-4     Document Type: Article

References (10)

1. [Ba] Baeumer, B. A Vector-Valued Operational Calculus and Abstract Cauchy Problems. Dissertation, Louisiana State University, 1997. (http://math.lsu.edu/̃tiger)
2. [B-L-N] Bäumer, B., G. Lumer, and F. Neubrander. Convolution kernels and generalized functions. Generalized functions, operator theory, and dynamical systems (Brussels, 1997), 68-78, Res. Notes Math. 399, Chapman & Hall/CRC, Boca Raton, FL, 1999. MR 2000a:44004
3. [B-N] Bäumer, B. and F. Neubrander. Laplace transform methods for evolution equations. Conferenze del Seminario di Matematica dell'Universitá di Bari, 259, 27-60, 1994. MR 97e:47119
4. [Do] Doetsch, G. Handbuch der Laplace Transformation. Vol. I-III, Birkhäuser Verlag, Basel-Stuttgart, 1950-1956. MR 13:230f; MR 18:35a; MR 18:894c
5. [Fo] Foiaş., C. Approximation des opérateurs de J. Mikusiński par des fonctions continues. Studio Mathematica 21, 73-74, 1961. MR 25:3334
6. [L-N] Lumer, G. and F. Neubrander. Asymptotic Laplace transforms and evolution equations. Evolution equations, Feshbach resonances, singular Hodge theory, 37-57, Math. Top. 16, Wiley-VCH, Berlin, 1999. MR 2000f:47068
7. [Mi] Mikusiński, J. Operational Calculus, v. 1-2, Pergamon Press, 2nd edition, 1987. MR 86b:44017; MR 88k:44010
8. [Sk] Skórnik, K. On the Foiaş, theorem on convolution of continuous functions, Complex Analysis and Applications '85 (Varna, 1985), 604-608, Publ. House Bulgar. Acad. Sci., Sofia, 1986. MR 89j:46057
9. [Ti] Titchmarsh, E. C. The zeros of certain integral functions. Proceedings of the London Mathematical Society 25 (1926), 283-302.
10. [Vi] Vignaux, J. C. Sugli integrali di Laplace asintotici, Atti Accad, naz. Lincei, Rend. Cl. Sci. fis. mat. (6) 29 (1939). 345-400.