On the Yosida approximation and the Widder-Arendt representation theorem

• Autorzy: Adam Bobrowski
• Języki publikacji: EN

Abstrakty

EN

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

Kategorie tematyczne

• 41A65: Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
• 44A10: Laplace transform
• 47D03: Groups and semigroups of linear operators

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 1997
• Tom: 124
• Numer: 3
• Strony: 281-290

Daty

wydano

1997

otrzymano

1996-05-13

Twórcy

autor

Adam Bobrowski

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

Bibliografia

• [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.