PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Annales Polonici Mathematici

1998 | 69 | 2 | 107-127
Tytuł artykułu

### A note on convergence of semigroups

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Convergence of semigroups which do not converge in the Trotter-Kato-Neveu sense is considered.
Słowa kluczowe
EN
Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
107-127
Opis fizyczny
Daty
wydano
1998
otrzymano
1997-04-28
Twórcy
autor
• Chair of Mathematics, Department of Electrical Engineering, Lublin Technical University, Nadbystrzycka 38a, 20-618 Lublin, Poland
Bibliografia
• [1] N. H. Abdelazis, A note on convergence of linear semigroups of class (1.A), Hokkaido Math. J. 18 (1989), 513-521.
• [2] N. H. Abdelazis, On approximation by discrete semigroups, J. Approx. Theory 73 (1993), 253-269.
• [3] N. H. Abdelazis and P. R. Chernoff, Continuous and discrete semigroup approximations with applications to the Cauchy problems, J. Operator Theory 32 (1994), 331-352.
• [4] W. Arendt, Vector-valued Laplace transforms and Cauchy problem, Israel J. Math. 59 (1987), 321-352.
• [5] W. Arendt and C. J. K. Batty, Tauberian theorems and stability of one-parameter semigroups, Trans. Amer. Math. Soc. 306 (1988), 837-852.
• [6] C. J. K. Batty, Some Tauberian theorems related to operator theory, in: Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., 1994, 21-34.
• [7] C. J. K. Batty, Asymptotic behaviour of semigroups, in: Banach Center Publ. 30, Inst. Math., Polish Acad. Sci., 1994, 35-52.
• [8] B. Bäumer and F. Neubrander, Laplace transform methods for evolution equations, Confer. Sem. Mat. Univ. Bari 1994, 27-60.
• [9] A. Bobrowski, Degenerate convergence of semigroups, Semigroup Forum 49 (1994), 303-327.
• [10] A. Bobrowski, Examples of a pointwise convergence of semigroups, Ann. Univ. Mariae Curie-Skłodowska Sect. A 49 (1995), 15-33.
• [11] A. Bobrowski, Integrated semigroups and the Trotter-Kato theorem, Bull. Polish Acad. Sci. Math. 41 (1994), 297-304.
• [12] A. Bobrowski, On the generation of non-continuous semigroups, Semigroup Forum 54 (1997), 237-252.
• [13] A. Bobrowski, On the Yosida approximation and the Widder-Arendt representation theorem, Studia Math. 124 (1997), 281-290.
• [14] A. Bobrowski, On approximation of (1.A) semigroups by discrete semigroups, Bull. Polish Acad. Sci. Math. 46 (1998), 141-154.
• [15] S. Busenberg and B. Wu, Convergence theorems for integrated semigroups, Differential Integral Equations 5 (1992), 509-520.
• [16] J. T. Cannon, Convergence criteria for a sequence of semi-groups, Appl. Anal. 5 (1975), 23-31.
• [17] P. J. Cohen, Factorization in group algebras, Duke Math. J. 26 (1959), 199-205.
• [18] P. C. Curtis and A. Figà-Talamanca, Factorization theorems for Banach algebras, in: Function Algebras, F. T. Birtel (ed.), Scott and Foresman, Chicago, 1966.
• [19] G. Da Prato and E. Sinestrari, Differential operators with non-dense domain, Ann. Scuola Norm. Sup. Pisa 14 (1987), 285-344.
• [20] E. B. Davies, One-Parameter Semigroups, Academic Press, London, 1980.
• [21] B. D. Doytchinov, W. J. Hrusa and S. J. Watson, On perturbation of differentiable semigroups, Semigroup Forum 54 (1997), 100-111.
• [22] N. Dunford, Spectral theory, I. Convergence to projections, Trans. Amer. Math. Soc. 54 (1943), 185-217.
• [23] S. N. Ethier and T. G. Kurtz, Markov Processes. Characterization and Convergence, Wiley Ser. Probab. Math. Statist., Wiley, New York, 1986.
• [24] A. Favini, J. A. Goldstein and S. Romanelli, Analytic semigroups on $L_w^p$ and on $L^p(0,1)$ generated by classes of second order differential operators, preprint, 1997.
• [25] J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Math. Monographs, 1985.
• [26] J. A. Goldstein, C. Radin and R. E. Showalter, Convergence rates of ergodic limits for semigroups and cosine operator functions, Semigroup Forum 16 (1978), 89-95.
• [27] E. Görlich and D. Pontzen, Approximation of operator semigroups of Oharu's class $C_(k)$, Tôhoku Math. J. (2) 34 (1982), 539-552.
• [28] S. L. Gulik, T. S. Liu and A. C. M. van Rooij, Group algebra modules II, Canad. J. Math. 19 (1967), 151-173.
• [29] B. Hennig and F. Neubrander, On representations, inversions and approximations of Laplace transform in Banach spaces, Appl. Anal. 49 (1993), 151-170.
• [30] E. Hewitt, The ranges of certain convolution operators, Math. Scand. 15 (1964) 147-155.
• [31] E. Hille, On the differentiability of semigroups of operators, Acta Sci. Math. (Szeged) 12 (1950), 19-24.
• [32] E. Hille and R. S. Phillips, Functional Analysis and Semi-Groups, rev. ed., Amer. Math. Soc. Collloq. Publ. 31, Providence, R.I., 1957.
• [33] K. Ito and H. P. Mc Kean, Jr., Diffusion Processes and Their Sample Paths, Springer, Berlin, 1965.
• [34] T. Kato, Perturbation Theory for Linear Operators, Springer, New York, 1966.
• [35] J. Kisyński, A proof of the Trotter-Kato theorem on approximation of semigroups, Colloq. Math. 18 (1967), 181-184.
• [36] J. Kisyński, Semigroups of operators and some of their applications to partial differential equations, in: Control Theory and Topics in Functional Analysis, Vol. 3, IAEA, Vienna, 1978, 305-405.
• [37] T. G. Kurtz, Extensions of Trotter's operator semigroup approximation theorems, J. Funct. Anal. 3 (1969), 354-375.
• [38] T. G. Kurtz, A general theorem on the convergence of operator semigroups, Trans. Amer. Math. Soc. 148 (1970), 23-32.
• [39] A. Lasota and R. Rudnicki, Asymptotic behaviour of semigroups of positive operators on C(X), Bull. Polish Acad. Sci. Math. 36 (1988), 151-159.
• [40] C. Lizama, On the convergence and approximation of integrated semigroups, J. Math. Anal. Appl. 181, (1994), 89-103.
• [41] G. Lumer, Solutions généralisées et semi-groupes intégrés, C. R. Acad. Sci. Paris Sér. I 310 (1990), 557-582.
• [42] G. Lumer, A (very) direct approach to locally Lipschitz continuous integrated semigroups and some related new results oriented towards applications, via generalized solutions, in: LSU Seminar Notes in Functional Analysis and PDEs, 1990-1991, Louisiana State Univ., Baton Rouge, 1991, 88-107.
• [43] G. Lumer, Evolution equations: Solutions for irregular evolution problems via generalized solutions and generalized initial values. Applications to periodic shocks models, Ann. Univ. Sarav. Ser. Math. 5 (1994), no. 1, 1-102.
• [44] Yu. I. Lyubich and V u Quôc Phóng, Asymptotic stability of linear differential equations on Banach spaces, Studia Math. 88 (1988), 37-42.
• [45] R. Nagel, One-Parameter Semigroups of Positive Operators, Lecture Notes in Math. 1184, Springer, Berlin, 1986.
• [46] J. Neveu, Théorie des semi-groupes de Markov, Univ. Calif. Publ. Statist. 2 (1958), 319-394.
• [47] A. Pazy, On the differentiability and compactness of semigroups of linear operators, J. Math. Mech. 17 (1960), 1131-1141.
• [48] A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Appl. Math. Sci. 44, Springer, New York, 1983.
• [49] R. S. Phillips, An inversion formula for the Laplace transform and semigroups of linear operators, Ann. of Math. 59 (1954), 325-356.
• [50] M. Renardy, On the stability of differentiability of semigroups, Semigroup Forum 51 (1995), 343-346.
• [51] G. M. Sklyar and V. Ya. Shirman, On the asymptotic stability of a linear differential equation in a Banach space, Teor. Funktsiĭ Funktsional. Anal. i Prilozhen. 37 (1982), 127-132 (in Russian).
• [52] M. Slemrod, Asymptotic behaviour of C₀ semi-groups as determined by the spectrum of the generator, Indiana Univ. Math. J. 25 (1976), 783-792.
• [53] T. Takahashi and S. Oharu, Approximation of operator semigroups in a Banach space, Tôhoku Math. J. 24 (1972), 505-528.
• [54] K. Yosida, On the differentiability of semigroups of linear operators, Proc. Japan Acad. 34 (1958), 337-340.
• [55] K. Yosida, Functional Analysis, Springer, Berlin, 1968.
Typ dokumentu
Bibliografia
Identyfikatory