ArticleOriginal scientific text

Title

On the Yosida approximation and the Widder-Arendt representation theorem

Authors 1

Affiliations

  1. Chair of Mathematics, Department of Electrical Engineering, Lublin Technical University, Nadbystrzycka 38A, 20-618 Lublin, Poland

Abstract

The Yosida approximation is treated as an inversion formula for the Laplace transform.

Bibliography

  1. W. Arendt, Vector-valued Laplace transforms and Cauchy problem, Israel J. Math. 59 (1987), 327-352.
  2. A. Bobrowski, Integrated semigroups and the Trotter-Kato theorem, Bull. Polish Acad. Sci. Math. 41 (1994), 297-304.
  3. G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248.
  4. C. Dellacherie and P. A. Meyer, Probabilities and Potential. C, North-Holland Math. Stud. 151, North-Holland, Amsterdam, 1988.
  5. H. O. Fattorini, A representation theorem for distribution semigroups, J. Funct. Anal. 6 (1970), 83-96.
  6. B. Hennig and F. Neubrander, On representations, inversions, and approximations of Laplace transforms in Banach spaces, Appl. Anal. 49 (1993), 151-170.
  7. E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I., 1957.
  8. F. Neubrander, The Laplace-Stieltjes transform in Banach spaces and abstract Cauchy problems, in: Proc. 3rd International Workshop Conference in Evolution Equations, Control Theory and Biomathematics, Han-sur-Lesse, P. Clément and G. Lumer (eds.), Lecture Notes in Pure and Appl. Math. 155, Dekker, 1994, 417-431.
  9. A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, 1983, Springer, New York, 1983.
  10. R. S. Phillips, An inversion formula for the Laplace transform and semigroups of linear operators, Ann. of Math. 59 (1954), 325-356.
  11. D. V. Widder, The Laplace Transform, Princeton Univ. Press, 1946.
  12. K. Yosida, Functional Analysis, Springer, Berlin, 1968.
Pages:
281-290
Main language of publication
English
Received
1996-05-13
Published
1997
Exact and natural sciences