# On the Yosida approximation and the Widder-Arendt representation theorem

Studia Mathematica (1997)

- Volume: 124, Issue: 3, page 281-290
- ISSN: 0039-3223

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topBobrowski, Adam. "On the Yosida approximation and the Widder-Arendt representation theorem." Studia Mathematica 124.3 (1997): 281-290. <http://eudml.org/doc/216415>.

@article{Bobrowski1997,

abstract = {The Yosida approximation is treated as an inversion formula for the Laplace transform.},

author = {Bobrowski, Adam},

journal = {Studia Mathematica},

keywords = {Widder-Arendt representation theorem; Laplace transform; Yosida approximation; continuous semigroups},

language = {eng},

number = {3},

pages = {281-290},

title = {On the Yosida approximation and the Widder-Arendt representation theorem},

url = {http://eudml.org/doc/216415},

volume = {124},

year = {1997},

}

TY - JOUR

AU - Bobrowski, Adam

TI - On the Yosida approximation and the Widder-Arendt representation theorem

JO - Studia Mathematica

PY - 1997

VL - 124

IS - 3

SP - 281

EP - 290

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

LA - eng

KW - Widder-Arendt representation theorem; Laplace transform; Yosida approximation; continuous semigroups

UR - http://eudml.org/doc/216415

ER -

## References

top- [1] W. Arendt, Vector-valued Laplace transforms and Cauchy problem, Israel J. Math. 59 (1987), 327-352. Zbl0637.44001
- [2] A. Bobrowski, Integrated semigroups and the Trotter-Kato theorem, Bull. Polish Acad. Sci. Math. 41 (1994), 297-304. Zbl0824.47031
- [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. Zbl0198.46504
- [6] B. Hennig and F. Neubrander, On representations, inversions, and approximations of Laplace transforms in Banach spaces, Appl. Anal. 49 (1993), 151-170. Zbl0791.44002
- [7] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, Amer. Math. Soc. Colloq. Publ. 31, Providence, R.I., 1957. Zbl0078.10004
- [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. Zbl0817.46046
- [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. Zbl0059.10704
- [11] D. V. Widder, The Laplace Transform, Princeton Univ. Press, 1946. Zbl0060.24801
- [12] K. Yosida, Functional Analysis, Springer, Berlin, 1968.

## Citations in EuDML Documents

top- Wojciech Chojnacki, Multiplier algebras, Banach bundles, and one-parameter semigroups
- Sten Bjon, On an integral transform by R. S. Phillips
- Jan Kisyński, Around Widder’s characterization of the Laplace transform of an element of ${L}^{\infty}\left({\mathbb{R}}^{+}\right)$
- Adam Bobrowski, A note on convergence of semigroups

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