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Global convoluted semigroups. (English) Zbl 1147.47028

From the authors’ summary: Global exponentially bounded convoluted semigroups in Banach spaces are systematically treated with the help of Laplace transform. A perturbation theorem in this context is proved and some characterizations of the introduced class of analytic convoluted semigroups are obtained. Illustrated examples of generators of convoluted semigroups, including differential operators, are presented.

MSC:

47D03 Groups and semigroups of linear operators
47D62 Integrated semigroups
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[1] Arendt, J. Math. Anal. Appl. 186 pp 572– (1994)
[2] Arendt, Semigroup Forum 45 pp 26– (1992)
[3] , , and , Vector-valued Laplace Transforms and Cauchy Problems, Monographs in Mathematics Vol. 96 (Birkhäuser, Basel, 2001). · Zbl 0978.34001
[4] Approximate solutions to the abstract Cauchy problem, in: Evolution Equations and their Applications in Physical and Life Sciences, Lecture Notes in Pure and Applied Mathematics Vol. 215 (Marcel Dekker, New York, 2001), pp. 33–41.
[5] , and , Convolution kernels and generalized functions, in: Generalized Functions, Operator Theory and Dynamical Systems, C. R. C. Research Notes in Mathematics Vol. 399 (Chapman & Hall, Boca Raton, FL, 1999).
[6] Beals, J. Funct. Anal. 10 pp 281– (1972)
[7] Beals, J. Funct. Anal. 10 pp 300– (1972)
[8] Chazarain, J. Funct. Anal. 7 pp 386– (1971)
[9] Ciorănescu, Bull. Sci. Math. 102 pp 167– (1978)
[10] Local convoluted semigroups, in: Evolution Equations (Baton Rauge, LA, 1992), pp. 107–122; reedited in 1995 by Marcel Dekker, New York.
[11] Cioranescu, prolongements, théorèmes de génération, C. R. Acad. Sci. Paris Sér. I Math. 319 pp 1273– (1995)
[12] and , On K (t)-convoluted semigroups, in: Recent Developments in Evolution Equations (Longman Sci. Tech., Harlow, 1995), pp. 86–93.
[13] Existence Families, Functional Calculi and Evolution Equations, Lecture Notes in Mathematics Vol. 1570 (Springer, Berlin, 1994). · Zbl 0811.47034
[14] deLaubenfels, Tokyo J. Math. 15 pp 17– (1992)
[15] von Grudzinski, Math. Nachr. 91 pp 297– (1979)
[16] Hieber, Forum Math. 3 pp 595– (1991)
[17] Kaiser, Arch. Math. (Basel) 81 pp 215– (2003) · Zbl 1065.47007 · doi:10.1007/s00013-003-0540-7
[18] Keyantuo, Proc. Edinb. Math. Soc. (2) 46 pp 395– (2003)
[19] Keyantuo, Proc. Edinb. Math. Soc. 46 pp 357– (2003)
[20] Komatsu, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 20 pp 25– (1973)
[21] Komatsu, J. Fac. Sci. Univ. Tokyo Sect. IA Math. 29 pp 653– (1982)
[22] Operational calculus and semi-groups of operators, in: Functional Analysis and related Topics (Springer, Berlin, 1991), pp. 213–234.
[23] Kostić, Bull. Cl. Sci. Math. Nat., Sci. Math. 28 pp 75– (2003)
[24] Convoluted and Distribution C -semigroups, Ph. D. thesis, University of Novi Sad (2004) (in Serbian).
[25] Kostić, Novi Sad J. Math. 35 pp 127– (2005)
[26] and , Ultradistribution and hyperfunction semigroups, preprint.
[27] and , Convoluted C -cosine functions and semigroups: relations with ultradistribution and hyperfunction sines, preprint. · Zbl 1171.47036
[28] Kunstmann, J. Operator Theory 37 pp 111– (1997)
[29] Kunstmann, Trans. Amer. Math. Soc. 351 pp 837– (1999)
[30] Banach space valued ultradistributions and applications to abstract Cauchy problems, preprint.
[31] Lectures on Entire Functions, Translations of Mathematical Monographs Vol. 150 (American Mathematical Society, Providence, RI, 1996).
[32] Li, Studia Math. 145 pp 265– (2001)
[33] Li, Studia Math. 154 pp 243– (2003)
[34] Li, J. Math. Soc. Japan 55 pp 1115– (2003)
[35] Lions, Portugal. Math. 19 pp 141– (1960)
[36] Lizama, J. Math. Anal. Appl. 243 pp 278– (2000)
[37] and , The asymptotic Laplace transform: new results and relation to Komatsu’s Laplace transform of hyperfunctions, in: Partial Differential Equations on Multistructures, Lecture Notes in Pure and Applied Mathematics Vol. 219 (Marcel Dekker, New York, 2001), pp. 147–162. · Zbl 0980.44003
[38] and , Abstract Cauchy Problems: Three Approaches (Chapman & Hall/CRC, Boca Raton, FL, 2001). · Zbl 0982.34001
[39] Miana, Studia Math. 166 pp 171– (2005)
[40] Miana, Forum Math. 14 pp 23– (2002)
[41] Müller, J. Math. Anal. Appl. 269 pp 401– (2002)
[42] Neubrander, Pacific J. Math. 135 pp 111– (1988) · Zbl 0675.47030 · doi:10.2140/pjm.1988.135.111
[43] Nicaise, J. Math. Anal. Appl. 180 pp 300– (1993)
[44] \={}O uchi, Proc. Japan Acad. Ser. A Math. Sci. 47 pp 541– (1971)
[45] Semigroups of Linear Operators and Applications to Partial Differential Equations (Springer-Verlag, Berlin, 1983).
[46] Pilipović, Boll. Un. Mat. Ital. B (7) 2 pp 235– (1988)
[47] Tanaka, J. Math. Anal. Appl. 170 pp 196– (1992)
[48] Tanaka, Proc. London Math. Soc. (3) 61 pp 63– (1990)
[49] Thieme, Adv. Math. Sci. Appl. 6 pp 445– (1996)
[50] van Neerven, Houston J. Math. 24 pp 137– (1998)
[51] Wang, J. Funct. Anal. 146 pp 352– (1997)
[52] Xiao, J. Funct. Anal. 172 pp 202– (2000)
[53] Xiao, J. Funct. Anal. 148 pp 448– (1997)
[54] and , The Cauchy Problem for Higher-order Abstract Differential Equations (Springer-Verlag, Berlin, 1998).
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