On the Yosida approximation and the Widder-Arendt representation theorem

Adam Bobrowski

Studia Mathematica (1997)

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

Abstract

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

How to cite

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Bobrowski, 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

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  1. [1] W. Arendt, Vector-valued Laplace transforms and Cauchy problem, Israel J. Math. 59 (1987), 327-352. Zbl0637.44001
  2. [2] A. Bobrowski, Integrated semigroups and the Trotter-Kato theorem, Bull. Polish Acad. Sci. Math. 41 (1994), 297-304. Zbl0824.47031
  3. [3] G. Da Prato, Semigruppi regolarizzabili, Ricerche Mat. 15 (1966), 223-248. 
  4. [4] C. Dellacherie and P. A. Meyer, Probabilities and Potential. C, North-Holland Math. Stud. 151, North-Holland, Amsterdam, 1988. 
  5. [5] H. O. Fattorini, A representation theorem for distribution semigroups, J. Funct. Anal. 6 (1970), 83-96. Zbl0198.46504
  6. [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. [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. [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. [9] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, 1983, Springer, New York, 1983. 
  10. [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. [11] D. V. Widder, The Laplace Transform, Princeton Univ. Press, 1946. Zbl0060.24801
  12. [12] K. Yosida, Functional Analysis, Springer, Berlin, 1968. 

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